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SubscribeUncertainty-aware Evaluation of Auxiliary Anomalies with the Expected Anomaly Posterior
Anomaly detection is the task of identifying examples that do not behave as expected. Because anomalies are rare and unexpected events, collecting real anomalous examples is often challenging in several applications. In addition, learning an anomaly detector with limited (or no) anomalies often yields poor prediction performance. One option is to employ auxiliary synthetic anomalies to improve the model training. However, synthetic anomalies may be of poor quality: anomalies that are unrealistic or indistinguishable from normal samples may deteriorate the detector's performance. Unfortunately, no existing methods quantify the quality of auxiliary anomalies. We fill in this gap and propose the expected anomaly posterior (EAP), an uncertainty-based score function that measures the quality of auxiliary anomalies by quantifying the total uncertainty of an anomaly detector. Experimentally on 40 benchmark datasets of images and tabular data, we show that EAP outperforms 12 adapted data quality estimators in the majority of cases.
Are Anomaly Scores Telling the Whole Story? A Benchmark for Multilevel Anomaly Detection
Anomaly detection (AD) is a machine learning task that identifies anomalies by learning patterns from normal training data. In many real-world scenarios, anomalies vary in severity, from minor anomalies with little risk to severe abnormalities requiring immediate attention. However, existing models primarily operate in a binary setting, and the anomaly scores they produce are usually based on the deviation of data points from normal data, which may not accurately reflect practical severity. In this paper, we address this gap by making three key contributions. First, we propose a novel setting, Multilevel AD (MAD), in which the anomaly score represents the severity of anomalies in real-world applications, and we highlight its diverse applications across various domains. Second, we introduce a novel benchmark, MAD-Bench, that evaluates models not only on their ability to detect anomalies, but also on how effectively their anomaly scores reflect severity. This benchmark incorporates multiple types of baselines and real-world applications involving severity. Finally, we conduct a comprehensive performance analysis on MAD-Bench. We evaluate models on their ability to assign severity-aligned scores, investigate the correspondence between their performance on binary and multilevel detection, and study their robustness. This analysis offers key insights into improving AD models for practical severity alignment. The code framework and datasets used for the benchmark will be made publicly available.
Deep Random Projection Outlyingness for Unsupervised Anomaly Detection
Random projection is a common technique for designing algorithms in a variety of areas, including information retrieval, compressive sensing and measuring of outlyingness. In this work, the original random projection outlyingness measure is modified and associated with a neural network to obtain an unsupervised anomaly detection method able to handle multimodal normality. Theoretical and experimental arguments are presented to justify the choice of the anomaly score estimator. The performance of the proposed neural network approach is comparable to a state-of-the-art anomaly detection method. Experiments conducted on the MNIST, Fashion-MNIST and CIFAR-10 datasets show the relevance of the proposed approach.
Estimating the Contamination Factor's Distribution in Unsupervised Anomaly Detection
Anomaly detection methods identify examples that do not follow the expected behaviour, typically in an unsupervised fashion, by assigning real-valued anomaly scores to the examples based on various heuristics. These scores need to be transformed into actual predictions by thresholding, so that the proportion of examples marked as anomalies equals the expected proportion of anomalies, called contamination factor. Unfortunately, there are no good methods for estimating the contamination factor itself. We address this need from a Bayesian perspective, introducing a method for estimating the posterior distribution of the contamination factor of a given unlabeled dataset. We leverage on outputs of several anomaly detectors as a representation that already captures the basic notion of anomalousness and estimate the contamination using a specific mixture formulation. Empirically on 22 datasets, we show that the estimated distribution is well-calibrated and that setting the threshold using the posterior mean improves the anomaly detectors' performance over several alternative methods. All code is publicly available for full reproducibility.
Can I trust my anomaly detection system? A case study based on explainable AI
Generative models based on variational autoencoders are a popular technique for detecting anomalies in images in a semi-supervised context. A common approach employs the anomaly score to detect the presence of anomalies, and it is known to reach high level of accuracy on benchmark datasets. However, since anomaly scores are computed from reconstruction disparities, they often obscure the detection of various spurious features, raising concerns regarding their actual efficacy. This case study explores the robustness of an anomaly detection system based on variational autoencoder generative models through the use of eXplainable AI methods. The goal is to get a different perspective on the real performances of anomaly detectors that use reconstruction differences. In our case study we discovered that, in many cases, samples are detected as anomalous for the wrong or misleading factors.
Development and Comparison of Scoring Functions in Curriculum Learning
Curriculum Learning is the presentation of samples to the machine learning model in a meaningful order instead of a random order. The main challenge of Curriculum Learning is determining how to rank these samples. The ranking of the samples is expressed by the scoring function. In this study, scoring functions were compared using data set features, using the model to be trained, and using another model and their ensemble versions. Experiments were performed for 4 images and 4 text datasets. No significant differences were found between scoring functions for text datasets, but significant improvements were obtained in scoring functions created using transfer learning compared to classical model training and other scoring functions for image datasets. It shows that different new scoring functions are waiting to be found for text classification tasks.
Deep Anomaly Detection under Labeling Budget Constraints
Selecting informative data points for expert feedback can significantly improve the performance of anomaly detection (AD) in various contexts, such as medical diagnostics or fraud detection. In this paper, we determine a set of theoretical conditions under which anomaly scores generalize from labeled queries to unlabeled data. Motivated by these results, we propose a data labeling strategy with optimal data coverage under labeling budget constraints. In addition, we propose a new learning framework for semi-supervised AD. Extensive experiments on image, tabular, and video data sets show that our approach results in state-of-the-art semi-supervised AD performance under labeling budget constraints.
CARE to Compare: A real-world dataset for anomaly detection in wind turbine data
Anomaly detection plays a crucial role in the field of predictive maintenance for wind turbines, yet the comparison of different algorithms poses a difficult task because domain specific public datasets are scarce. Many comparisons of different approaches either use benchmarks composed of data from many different domains, inaccessible data or one of the few publicly available datasets which lack detailed information about the faults. Moreover, many publications highlight a couple of case studies where fault detection was successful. With this paper we publish a high quality dataset that contains data from 36 wind turbines across 3 different wind farms as well as the most detailed fault information of any public wind turbine dataset as far as we know. The new dataset contains 89 years worth of real-world operating data of wind turbines, distributed across 44 labeled time frames for anomalies that led up to faults, as well as 51 time series representing normal behavior. Additionally, the quality of training data is ensured by turbine-status-based labels for each data point. Furthermore, we propose a new scoring method, called CARE (Coverage, Accuracy, Reliability and Earliness), which takes advantage of the information depth that is present in the dataset to identify a good all-around anomaly detection model. This score considers the anomaly detection performance, the ability to recognize normal behavior properly and the capability to raise as few false alarms as possible while simultaneously detecting anomalies early.
PATE: Proximity-Aware Time series anomaly Evaluation
Evaluating anomaly detection algorithms in time series data is critical as inaccuracies can lead to flawed decision-making in various domains where real-time analytics and data-driven strategies are essential. Traditional performance metrics assume iid data and fail to capture the complex temporal dynamics and specific characteristics of time series anomalies, such as early and delayed detections. We introduce Proximity-Aware Time series anomaly Evaluation (PATE), a novel evaluation metric that incorporates the temporal relationship between prediction and anomaly intervals. PATE uses proximity-based weighting considering buffer zones around anomaly intervals, enabling a more detailed and informed assessment of a detection. Using these weights, PATE computes a weighted version of the area under the Precision and Recall curve. Our experiments with synthetic and real-world datasets show the superiority of PATE in providing more sensible and accurate evaluations than other evaluation metrics. We also tested several state-of-the-art anomaly detectors across various benchmark datasets using the PATE evaluation scheme. The results show that a common metric like Point-Adjusted F1 Score fails to characterize the detection performances well, and that PATE is able to provide a more fair model comparison. By introducing PATE, we redefine the understanding of model efficacy that steers future studies toward developing more effective and accurate detection models.
MuSc: Zero-Shot Industrial Anomaly Classification and Segmentation with Mutual Scoring of the Unlabeled Images
This paper studies zero-shot anomaly classification (AC) and segmentation (AS) in industrial vision. We reveal that the abundant normal and abnormal cues implicit in unlabeled test images can be exploited for anomaly determination, which is ignored by prior methods. Our key observation is that for the industrial product images, the normal image patches could find a relatively large number of similar patches in other unlabeled images, while the abnormal ones only have a few similar patches. We leverage such a discriminative characteristic to design a novel zero-shot AC/AS method by Mutual Scoring (MuSc) of the unlabeled images, which does not need any training or prompts. Specifically, we perform Local Neighborhood Aggregation with Multiple Degrees (LNAMD) to obtain the patch features that are capable of representing anomalies in varying sizes. Then we propose the Mutual Scoring Mechanism (MSM) to leverage the unlabeled test images to assign the anomaly score to each other. Furthermore, we present an optimization approach named Re-scoring with Constrained Image-level Neighborhood (RsCIN) for image-level anomaly classification to suppress the false positives caused by noises in normal images. The superior performance on the challenging MVTec AD and VisA datasets demonstrates the effectiveness of our approach. Compared with the state-of-the-art zero-shot approaches, MuSc achieves a 21.1% PRO absolute gain (from 72.7% to 93.8%) on MVTec AD, a 19.4% pixel-AP gain and a 14.7% pixel-AUROC gain on VisA. In addition, our zero-shot approach outperforms most of the few-shot approaches and is comparable to some one-class methods. Code is available at https://github.com/xrli-U/MuSc.
Neural network approach to classifying alarming student responses to online assessment
Automated scoring engines are increasingly being used to score the free-form text responses that students give to questions. Such engines are not designed to appropriately deal with responses that a human reader would find alarming such as those that indicate an intention to self-harm or harm others, responses that allude to drug abuse or sexual abuse or any response that would elicit concern for the student writing the response. Our neural network models have been designed to help identify these anomalous responses from a large collection of typical responses that students give. The responses identified by the neural network can be assessed for urgency, severity, and validity more quickly by a team of reviewers than otherwise possible. Given the anomalous nature of these types of responses, our goal is to maximize the chance of flagging these responses for review given the constraint that only a fixed percentage of responses can viably be assessed by a team of reviewers.
AUPIMO: Redefining Visual Anomaly Detection Benchmarks with High Speed and Low Tolerance
Recent advances in visual anomaly detection research have seen AUROC and AUPRO scores on public benchmark datasets such as MVTec and VisA converge towards perfect recall, giving the impression that these benchmarks are near-solved. However, high AUROC and AUPRO scores do not always reflect qualitative performance, which limits the validity of these metrics in real-world applications. We argue that the artificial ceiling imposed by the lack of an adequate evaluation metric restrains progression of the field, and it is crucial that we revisit the evaluation metrics used to rate our algorithms. In response, we introduce Per-IMage Overlap (PIMO), a novel metric that addresses the shortcomings of AUROC and AUPRO. PIMO retains the recall-based nature of the existing metrics but introduces two distinctions: the assignment of curves (and respective area under the curve) is per-image, and its X-axis relies solely on normal images. Measuring recall per image simplifies instance score indexing and is more robust to noisy annotations. As we show, it also accelerates computation and enables the usage of statistical tests to compare models. By imposing low tolerance for false positives on normal images, PIMO provides an enhanced model validation procedure and highlights performance variations across datasets. Our experiments demonstrate that PIMO offers practical advantages and nuanced performance insights that redefine anomaly detection benchmarks -- notably challenging the perception that MVTec AD and VisA datasets have been solved by contemporary models. Available on GitHub: https://github.com/jpcbertoldo/aupimo.
Real-world Anomaly Detection in Surveillance Videos
Surveillance videos are able to capture a variety of realistic anomalies. In this paper, we propose to learn anomalies by exploiting both normal and anomalous videos. To avoid annotating the anomalous segments or clips in training videos, which is very time consuming, we propose to learn anomaly through the deep multiple instance ranking framework by leveraging weakly labeled training videos, i.e. the training labels (anomalous or normal) are at video-level instead of clip-level. In our approach, we consider normal and anomalous videos as bags and video segments as instances in multiple instance learning (MIL), and automatically learn a deep anomaly ranking model that predicts high anomaly scores for anomalous video segments. Furthermore, we introduce sparsity and temporal smoothness constraints in the ranking loss function to better localize anomaly during training. We also introduce a new large-scale first of its kind dataset of 128 hours of videos. It consists of 1900 long and untrimmed real-world surveillance videos, with 13 realistic anomalies such as fighting, road accident, burglary, robbery, etc. as well as normal activities. This dataset can be used for two tasks. First, general anomaly detection considering all anomalies in one group and all normal activities in another group. Second, for recognizing each of 13 anomalous activities. Our experimental results show that our MIL method for anomaly detection achieves significant improvement on anomaly detection performance as compared to the state-of-the-art approaches. We provide the results of several recent deep learning baselines on anomalous activity recognition. The low recognition performance of these baselines reveals that our dataset is very challenging and opens more opportunities for future work. The dataset is available at: https://webpages.uncc.edu/cchen62/dataset.html
Deep Sets
We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.
Language-guided Open-world Video Anomaly Detection
Video anomaly detection models aim to detect anomalies that deviate from what is expected. In open-world scenarios, the expected events may change as requirements change. For example, not wearing a mask is considered abnormal during a flu outbreak but normal otherwise. However, existing methods assume that the definition of anomalies is invariable, and thus are not applicable to the open world. To address this, we propose a novel open-world VAD paradigm with variable definitions, allowing guided detection through user-provided natural language at inference time. This paradigm necessitates establishing a robust mapping from video and textual definition to anomaly score. Therefore, we propose LaGoVAD (Language-guided Open-world VAD), a model that dynamically adapts anomaly definitions through two regularization strategies: diversifying the relative durations of anomalies via dynamic video synthesis, and enhancing feature robustness through contrastive learning with negative mining. Training such adaptable models requires diverse anomaly definitions, but existing datasets typically provide given labels without semantic descriptions. To bridge this gap, we collect PreVAD (Pre-training Video Anomaly Dataset), the largest and most diverse video anomaly dataset to date, featuring 35,279 annotated videos with multi-level category labels and descriptions that explicitly define anomalies. Zero-shot experiments on seven datasets demonstrate SOTA performance. Data and code will be released.
Examining the Source of Defects from a Mechanical Perspective for 3D Anomaly Detection
In this paper, we explore a novel approach to 3D anomaly detection (AD) that goes beyond merely identifying anomalies based on structural characteristics. Our primary perspective is that most anomalies arise from unpredictable defective forces originating from both internal and external sources. To address these anomalies, we seek out opposing forces that can help correct them. Therefore, we introduce the Mechanics Complementary Model-based Framework for the 3D-AD task (MC4AD), which generates internal and external corrective forces for each point. We first propose a Diverse Anomaly-Generation (DA-Gen) module designed to simulate various types of anomalies. Next, we present the Corrective Force Prediction Network (CFP-Net), which uses complementary representations for point-level analysis to simulate the different contributions from internal and external corrective forces. To ensure the corrective forces are constrained effectively, we have developed a combined loss function that includes a new symmetric loss and an overall loss. Notably, we implement a Hierarchical Quality Control (HQC) strategy based on a three-way decision process and contribute a dataset titled Anomaly-IntraVariance, which incorporates intraclass variance to evaluate our model. As a result, the proposed MC4AD has been proven effective through theory and experimentation. The experimental results demonstrate that our approach yields nine state-of-the-art performances, achieving optimal results with minimal parameters and the fastest inference speed across five existing datasets, in addition to the proposed Anomaly-IntraVariance dataset. The source is available at https://github.com/hzzzzzhappy/MC4AD
Modeling the Distribution of Normal Data in Pre-Trained Deep Features for Anomaly Detection
Anomaly Detection (AD) in images is a fundamental computer vision problem and refers to identifying images and image substructures that deviate significantly from the norm. Popular AD algorithms commonly try to learn a model of normality from scratch using task specific datasets, but are limited to semi-supervised approaches employing mostly normal data due to the inaccessibility of anomalies on a large scale combined with the ambiguous nature of anomaly appearance. We follow an alternative approach and demonstrate that deep feature representations learned by discriminative models on large natural image datasets are well suited to describe normality and detect even subtle anomalies in a transfer learning setting. Our model of normality is established by fitting a multivariate Gaussian (MVG) to deep feature representations of classification networks trained on ImageNet using normal data only. By subsequently applying the Mahalanobis distance as the anomaly score we outperform the current state of the art on the public MVTec AD dataset, achieving an AUROC value of 95.8 pm 1.2 (mean pm SEM) over all 15 classes. We further investigate why the learned representations are discriminative to the AD task using Principal Component Analysis. We find that the principal components containing little variance in normal data are the ones crucial for discriminating between normal and anomalous instances. This gives a possible explanation to the often sub-par performance of AD approaches trained from scratch using normal data only. By selectively fitting a MVG to these most relevant components only, we are able to further reduce model complexity while retaining AD performance. We also investigate setting the working point by selecting acceptable False Positive Rate thresholds based on the MVG assumption. Code available at https://github.com/ORippler/gaussian-ad-mvtec
Subset Selection Based On Multiple Rankings in the Presence of Bias: Effectiveness of Fairness Constraints for Multiwinner Voting Score Functions
We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest ``quality'' subset. Score functions from the multiwinner voting literature have been used to aggregate rankings into quality scores for subsets. We study this setting of subset selection problems when, in addition, rankings may contain systemic or unconscious biases toward a group of items. For a general model of input rankings and biases, we show that requiring the selected subset to satisfy group fairness constraints can improve the quality of the selection with respect to unbiased rankings. Importantly, we show that for fairness constraints to be effective, different multiwinner score functions may require a drastically different number of rankings: While for some functions, fairness constraints need an exponential number of rankings to recover a close-to-optimal solution, for others, this dependency is only polynomial. This result relies on a novel notion of ``smoothness'' of submodular functions in this setting that quantifies how well a function can ``correctly'' assess the quality of items in the presence of bias. The results in this paper can be used to guide the choice of multiwinner score functions for the subset selection setting considered here; we additionally provide a tool to empirically enable this.
Sampling Multimodal Distributions with the Vanilla Score: Benefits of Data-Based Initialization
There is a long history, as well as a recent explosion of interest, in statistical and generative modeling approaches based on score functions -- derivatives of the log-likelihood of a distribution. In seminal works, Hyv\"arinen proposed vanilla score matching as a way to learn distributions from data by computing an estimate of the score function of the underlying ground truth, and established connections between this method and established techniques like Contrastive Divergence and Pseudolikelihood estimation. It is by now well-known that vanilla score matching has significant difficulties learning multimodal distributions. Although there are various ways to overcome this difficulty, the following question has remained unanswered -- is there a natural way to sample multimodal distributions using just the vanilla score? Inspired by a long line of related experimental works, we prove that the Langevin diffusion with early stopping, initialized at the empirical distribution, and run on a score function estimated from data successfully generates natural multimodal distributions (mixtures of log-concave distributions).
ConjNorm: Tractable Density Estimation for Out-of-Distribution Detection
Post-hoc out-of-distribution (OOD) detection has garnered intensive attention in reliable machine learning. Many efforts have been dedicated to deriving score functions based on logits, distances, or rigorous data distribution assumptions to identify low-scoring OOD samples. Nevertheless, these estimate scores may fail to accurately reflect the true data density or impose impractical constraints. To provide a unified perspective on density-based score design, we propose a novel theoretical framework grounded in Bregman divergence, which extends distribution considerations to encompass an exponential family of distributions. Leveraging the conjugation constraint revealed in our theorem, we introduce a ConjNorm method, reframing density function design as a search for the optimal norm coefficient p against the given dataset. In light of the computational challenges of normalization, we devise an unbiased and analytically tractable estimator of the partition function using the Monte Carlo-based importance sampling technique. Extensive experiments across OOD detection benchmarks empirically demonstrate that our proposed ConjNorm has established a new state-of-the-art in a variety of OOD detection setups, outperforming the current best method by up to 13.25% and 28.19% (FPR95) on CIFAR-100 and ImageNet-1K, respectively.
PNI : Industrial Anomaly Detection using Position and Neighborhood Information
Because anomalous samples cannot be used for training, many anomaly detection and localization methods use pre-trained networks and non-parametric modeling to estimate encoded feature distribution. However, these methods neglect the impact of position and neighborhood information on the distribution of normal features. To overcome this, we propose a new algorithm, PNI, which estimates the normal distribution using conditional probability given neighborhood features, modeled with a multi-layer perceptron network. Moreover, position information is utilized by creating a histogram of representative features at each position. Instead of simply resizing the anomaly map, the proposed method employs an additional refine network trained on synthetic anomaly images to better interpolate and account for the shape and edge of the input image. We conducted experiments on the MVTec AD benchmark dataset and achieved state-of-the-art performance, with 99.56\% and 98.98\% AUROC scores in anomaly detection and localization, respectively.
Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization
Diffusion models have emerged as a powerful tool rivaling GANs in generating high-quality samples with improved fidelity, flexibility, and robustness. A key component of these models is to learn the score function through score matching. Despite empirical success on various tasks, it remains unclear whether gradient-based algorithms can learn the score function with a provable accuracy. As a first step toward answering this question, this paper establishes a mathematical framework for analyzing score estimation using neural networks trained by gradient descent. Our analysis covers both the optimization and the generalization aspects of the learning procedure. In particular, we propose a parametric form to formulate the denoising score-matching problem as a regression with noisy labels. Compared to the standard supervised learning setup, the score-matching problem introduces distinct challenges, including unbounded input, vector-valued output, and an additional time variable, preventing existing techniques from being applied directly. In this paper, we show that with proper designs, the evolution of neural networks during training can be accurately modeled by a series of kernel regression tasks. Furthermore, by applying an early-stopping rule for gradient descent and leveraging recent developments in neural tangent kernels, we establish the first generalization error (sample complexity) bounds for learning the score function with neural networks, despite the presence of noise in the observations. Our analysis is grounded in a novel parametric form of the neural network and an innovative connection between score matching and regression analysis, facilitating the application of advanced statistical and optimization techniques.
SCoRe: Submodular Combinatorial Representation Learning
In this paper we introduce the SCoRe (Submodular Combinatorial Representation Learning) framework, a novel approach in representation learning that addresses inter-class bias and intra-class variance. SCoRe provides a new combinatorial viewpoint to representation learning, by introducing a family of loss functions based on set-based submodular information measures. We develop two novel combinatorial formulations for loss functions, using the Total Information and Total Correlation, that naturally minimize intra-class variance and inter-class bias. Several commonly used metric/contrastive learning loss functions like supervised contrastive loss, orthogonal projection loss, and N-pairs loss, are all instances of SCoRe, thereby underlining the versatility and applicability of SCoRe in a broad spectrum of learning scenarios. Novel objectives in SCoRe naturally model class-imbalance with up to 7.6\% improvement in classification on CIFAR-10-LT, CIFAR-100-LT, MedMNIST, 2.1% on ImageNet-LT, and 19.4% in object detection on IDD and LVIS (v1.0), demonstrating its effectiveness over existing approaches.
Test Time Training for Industrial Anomaly Segmentation
Anomaly Detection and Segmentation (AD&S) is crucial for industrial quality control. While existing methods excel in generating anomaly scores for each pixel, practical applications require producing a binary segmentation to identify anomalies. Due to the absence of labeled anomalies in many real scenarios, standard practices binarize these maps based on some statistics derived from a validation set containing only nominal samples, resulting in poor segmentation performance. This paper addresses this problem by proposing a test time training strategy to improve the segmentation performance. Indeed, at test time, we can extract rich features directly from anomalous samples to train a classifier that can discriminate defects effectively. Our general approach can work downstream to any AD&S method that provides an anomaly score map as output, even in multimodal settings. We demonstrate the effectiveness of our approach over baselines through extensive experimentation and evaluation on MVTec AD and MVTec 3D-AD.
An Informal Introduction to Multiplet Neural Networks
In the artificial neuron, I replace the dot product with the weighted Lehmer mean, which may emulate different cases of a generalized mean. The single neuron instance is replaced by a multiplet of neurons which have the same averaging weights. A group of outputs feed forward, in lieu of the single scalar. The generalization parameter is typically set to a different value for each neuron in the multiplet. I further extend the concept to a multiplet taken from the Gini mean. Derivatives with respect to the weight parameters and with respect to the two generalization parameters are given. Some properties of the network are investigated, showing the capacity to emulate the classical exclusive-or problem organically in two layers and perform some multiplication and division. The network can instantiate truncated power series and variants, which can be used to approximate different functions, provided that parameters are constrained. Moreover, a mean case slope score is derived that can facilitate a learning-rate novelty based on homogeneity of the selected elements. The multiplet neuron equation provides a way to segment regularization timeframes and approaches.
MuSc-V2: Zero-Shot Multimodal Industrial Anomaly Classification and Segmentation with Mutual Scoring of Unlabeled Samples
Zero-shot anomaly classification (AC) and segmentation (AS) methods aim to identify and outline defects without using any labeled samples. In this paper, we reveal a key property that is overlooked by existing methods: normal image patches across industrial products typically find many other similar patches, not only in 2D appearance but also in 3D shapes, while anomalies remain diverse and isolated. To explicitly leverage this discriminative property, we propose a Mutual Scoring framework (MuSc-V2) for zero-shot AC/AS, which flexibly supports single 2D/3D or multimodality. Specifically, our method begins by improving 3D representation through Iterative Point Grouping (IPG), which reduces false positives from discontinuous surfaces. Then we use Similarity Neighborhood Aggregation with Multi-Degrees (SNAMD) to fuse 2D/3D neighborhood cues into more discriminative multi-scale patch features for mutual scoring. The core comprises a Mutual Scoring Mechanism (MSM) that lets samples within each modality to assign score to each other, and Cross-modal Anomaly Enhancement (CAE) that fuses 2D and 3D scores to recover modality-specific missing anomalies. Finally, Re-scoring with Constrained Neighborhood (RsCon) suppresses false classification based on similarity to more representative samples. Our framework flexibly works on both the full dataset and smaller subsets with consistently robust performance, ensuring seamless adaptability across diverse product lines. In aid of the novel framework, MuSc-V2 achieves significant performance improvements: a +23.7% AP gain on the MVTec 3D-AD dataset and a +19.3% boost on the Eyecandies dataset, surpassing previous zero-shot benchmarks and even outperforming most few-shot methods. The code will be available at The code will be available at https://github.com/HUST-SLOW/MuSc-V2{https://github.com/HUST-SLOW/MuSc-V2}.
Equivariant Scalar Fields for Molecular Docking with Fast Fourier Transforms
Molecular docking is critical to structure-based virtual screening, yet the throughput of such workflows is limited by the expensive optimization of scoring functions involved in most docking algorithms. We explore how machine learning can accelerate this process by learning a scoring function with a functional form that allows for more rapid optimization. Specifically, we define the scoring function to be the cross-correlation of multi-channel ligand and protein scalar fields parameterized by equivariant graph neural networks, enabling rapid optimization over rigid-body degrees of freedom with fast Fourier transforms. The runtime of our approach can be amortized at several levels of abstraction, and is particularly favorable for virtual screening settings with a common binding pocket. We benchmark our scoring functions on two simplified docking-related tasks: decoy pose scoring and rigid conformer docking. Our method attains similar but faster performance on crystal structures compared to the widely-used Vina and Gnina scoring functions, and is more robust on computationally predicted structures. Code is available at https://github.com/bjing2016/scalar-fields.
Concise Logarithmic Loss Function for Robust Training of Anomaly Detection Model
Recently, deep learning-based algorithms are widely adopted due to the advantage of being able to establish anomaly detection models without or with minimal domain knowledge of the task. Instead, to train the artificial neural network more stable, it should be better to define the appropriate neural network structure or the loss function. For the training anomaly detection model, the mean squared error (MSE) function is adopted widely. On the other hand, the novel loss function, logarithmic mean squared error (LMSE), is proposed in this paper to train the neural network more stable. This study covers a variety of comparisons from mathematical comparisons, visualization in the differential domain for backpropagation, loss convergence in the training process, and anomaly detection performance. In an overall view, LMSE is superior to the existing MSE function in terms of strongness of loss convergence, anomaly detection performance. The LMSE function is expected to be applicable for training not only the anomaly detection model but also the general generative neural network.
Making Reconstruction-based Method Great Again for Video Anomaly Detection
Anomaly detection in videos is a significant yet challenging problem. Previous approaches based on deep neural networks employ either reconstruction-based or prediction-based approaches. Nevertheless, existing reconstruction-based methods 1) rely on old-fashioned convolutional autoencoders and are poor at modeling temporal dependency; 2) are prone to overfit the training samples, leading to indistinguishable reconstruction errors of normal and abnormal frames during the inference phase. To address such issues, firstly, we get inspiration from transformer and propose {textbf S}patio-{textbf T}emporal {textbf A}uto-{textbf T}rans-{textbf E}ncoder, dubbed as STATE, as a new autoencoder model for enhanced consecutive frame reconstruction. Our STATE is equipped with a specifically designed learnable convolutional attention module for efficient temporal learning and reasoning. Secondly, we put forward a novel reconstruction-based input perturbation technique during testing to further differentiate anomalous frames. With the same perturbation magnitude, the testing reconstruction error of the normal frames lowers more than that of the abnormal frames, which contributes to mitigating the overfitting problem of reconstruction. Owing to the high relevance of the frame abnormality and the objects in the frame, we conduct object-level reconstruction using both the raw frame and the corresponding optical flow patches. Finally, the anomaly score is designed based on the combination of the raw and motion reconstruction errors using perturbed inputs. Extensive experiments on benchmark video anomaly detection datasets demonstrate that our approach outperforms previous reconstruction-based methods by a notable margin, and achieves state-of-the-art anomaly detection performance consistently. The code is available at https://github.com/wyzjack/MRMGA4VAD.
Normal-Abnormal Guided Generalist Anomaly Detection
Generalist Anomaly Detection (GAD) aims to train a unified model on an original domain that can detect anomalies in new target domains. Previous GAD methods primarily use only normal samples as references, overlooking the valuable information contained in anomalous samples that are often available in real-world scenarios. To address this limitation, we propose a more practical approach: normal-abnormal-guided generalist anomaly detection, which leverages both normal and anomalous samples as references to guide anomaly detection across diverse domains. We introduce the Normal-Abnormal Generalist Learning (NAGL) framework, consisting of two key components: Residual Mining (RM) and Anomaly Feature Learning (AFL). RM extracts abnormal patterns from normal-abnormal reference residuals to establish transferable anomaly representations, while AFL adaptively learns anomaly features in query images through residual mapping to identify instance-aware anomalies. Our approach effectively utilizes both normal and anomalous references for more accurate and efficient cross-domain anomaly detection. Extensive experiments across multiple benchmarks demonstrate that our method significantly outperforms existing GAD approaches. This work represents the first to adopt a mixture of normal and abnormal samples as references in generalist anomaly detection. The code and datasets are available at https://github.com/JasonKyng/NAGL.
Multiscale Score Matching for Out-of-Distribution Detection
We present a new methodology for detecting out-of-distribution (OOD) images by utilizing norms of the score estimates at multiple noise scales. A score is defined to be the gradient of the log density with respect to the input data. Our methodology is completely unsupervised and follows a straight forward training scheme. First, we train a deep network to estimate scores for levels of noise. Once trained, we calculate the noisy score estimates for N in-distribution samples and take the L2-norms across the input dimensions (resulting in an NxL matrix). Then we train an auxiliary model (such as a Gaussian Mixture Model) to learn the in-distribution spatial regions in this L-dimensional space. This auxiliary model can now be used to identify points that reside outside the learned space. Despite its simplicity, our experiments show that this methodology significantly outperforms the state-of-the-art in detecting out-of-distribution images. For example, our method can effectively separate CIFAR-10 (inlier) and SVHN (OOD) images, a setting which has been previously shown to be difficult for deep likelihood models.
Towards Training-free Anomaly Detection with Vision and Language Foundation Models
Anomaly detection is valuable for real-world applications, such as industrial quality inspection. However, most approaches focus on detecting local structural anomalies while neglecting compositional anomalies incorporating logical constraints. In this paper, we introduce LogSAD, a novel multi-modal framework that requires no training for both Logical and Structural Anomaly Detection. First, we propose a match-of-thought architecture that employs advanced large multi-modal models (i.e. GPT-4V) to generate matching proposals, formulating interests and compositional rules of thought for anomaly detection. Second, we elaborate on multi-granularity anomaly detection, consisting of patch tokens, sets of interests, and composition matching with vision and language foundation models. Subsequently, we present a calibration module to align anomaly scores from different detectors, followed by integration strategies for the final decision. Consequently, our approach addresses both logical and structural anomaly detection within a unified framework and achieves state-of-the-art results without the need for training, even when compared to supervised approaches, highlighting its robustness and effectiveness. Code is available at https://github.com/zhang0jhon/LogSAD.
Anomaly Detection under Distribution Shift
Anomaly detection (AD) is a crucial machine learning task that aims to learn patterns from a set of normal training samples to identify abnormal samples in test data. Most existing AD studies assume that the training and test data are drawn from the same data distribution, but the test data can have large distribution shifts arising in many real-world applications due to different natural variations such as new lighting conditions, object poses, or background appearances, rendering existing AD methods ineffective in such cases. In this paper, we consider the problem of anomaly detection under distribution shift and establish performance benchmarks on three widely-used AD and out-of-distribution (OOD) generalization datasets. We demonstrate that simple adaptation of state-of-the-art OOD generalization methods to AD settings fails to work effectively due to the lack of labeled anomaly data. We further introduce a novel robust AD approach to diverse distribution shifts by minimizing the distribution gap between in-distribution and OOD normal samples in both the training and inference stages in an unsupervised way. Our extensive empirical results on the three datasets show that our approach substantially outperforms state-of-the-art AD methods and OOD generalization methods on data with various distribution shifts, while maintaining the detection accuracy on in-distribution data.
Entity Embedding-based Anomaly Detection for Heterogeneous Categorical Events
Anomaly detection plays an important role in modern data-driven security applications, such as detecting suspicious access to a socket from a process. In many cases, such events can be described as a collection of categorical values that are considered as entities of different types, which we call heterogeneous categorical events. Due to the lack of intrinsic distance measures among entities, and the exponentially large event space, most existing work relies heavily on heuristics to calculate abnormal scores for events. Different from previous work, we propose a principled and unified probabilistic model APE (Anomaly detection via Probabilistic pairwise interaction and Entity embedding) that directly models the likelihood of events. In this model, we embed entities into a common latent space using their observed co-occurrence in different events. More specifically, we first model the compatibility of each pair of entities according to their embeddings. Then we utilize the weighted pairwise interactions of different entity types to define the event probability. Using Noise-Contrastive Estimation with "context-dependent" noise distribution, our model can be learned efficiently regardless of the large event space. Experimental results on real enterprise surveillance data show that our methods can accurately detect abnormal events compared to other state-of-the-art abnormal detection techniques.
Empirical study of Machine Learning Classifier Evaluation Metrics behavior in Massively Imbalanced and Noisy data
With growing credit card transaction volumes, the fraud percentages are also rising, including overhead costs for institutions to combat and compensate victims. The use of machine learning into the financial sector permits more effective protection against fraud and other economic crime. Suitably trained machine learning classifiers help proactive fraud detection, improving stakeholder trust and robustness against illicit transactions. However, the design of machine learning based fraud detection algorithms has been challenging and slow due the massively unbalanced nature of fraud data and the challenges of identifying the frauds accurately and completely to create a gold standard ground truth. Furthermore, there are no benchmarks or standard classifier evaluation metrics to measure and identify better performing classifiers, thus keeping researchers in the dark. In this work, we develop a theoretical foundation to model human annotation errors and extreme imbalance typical in real world fraud detection data sets. By conducting empirical experiments on a hypothetical classifier, with a synthetic data distribution approximated to a popular real world credit card fraud data set, we simulate human annotation errors and extreme imbalance to observe the behavior of popular machine learning classifier evaluation matrices. We demonstrate that a combined F1 score and g-mean, in that specific order, is the best evaluation metric for typical imbalanced fraud detection model classification.
StRegA: Unsupervised Anomaly Detection in Brain MRIs using a Compact Context-encoding Variational Autoencoder
Expert interpretation of anatomical images of the human brain is the central part of neuro-radiology. Several machine learning-based techniques have been proposed to assist in the analysis process. However, the ML models typically need to be trained to perform a specific task, e.g., brain tumour segmentation or classification. Not only do the corresponding training data require laborious manual annotations, but a wide variety of abnormalities can be present in a human brain MRI - even more than one simultaneously, which renders representation of all possible anomalies very challenging. Hence, a possible solution is an unsupervised anomaly detection (UAD) system that can learn a data distribution from an unlabelled dataset of healthy subjects and then be applied to detect out of distribution samples. Such a technique can then be used to detect anomalies - lesions or abnormalities, for example, brain tumours, without explicitly training the model for that specific pathology. Several Variational Autoencoder (VAE) based techniques have been proposed in the past for this task. Even though they perform very well on controlled artificially simulated anomalies, many of them perform poorly while detecting anomalies in clinical data. This research proposes a compact version of the "context-encoding" VAE (ceVAE) model, combined with pre and post-processing steps, creating a UAD pipeline (StRegA), which is more robust on clinical data, and shows its applicability in detecting anomalies such as tumours in brain MRIs. The proposed pipeline achieved a Dice score of 0.642pm0.101 while detecting tumours in T2w images of the BraTS dataset and 0.859pm0.112 while detecting artificially induced anomalies, while the best performing baseline achieved 0.522pm0.135 and 0.783pm0.111, respectively.
MOODv2: Masked Image Modeling for Out-of-Distribution Detection
The crux of effective out-of-distribution (OOD) detection lies in acquiring a robust in-distribution (ID) representation, distinct from OOD samples. While previous methods predominantly leaned on recognition-based techniques for this purpose, they often resulted in shortcut learning, lacking comprehensive representations. In our study, we conducted a comprehensive analysis, exploring distinct pretraining tasks and employing various OOD score functions. The results highlight that the feature representations pre-trained through reconstruction yield a notable enhancement and narrow the performance gap among various score functions. This suggests that even simple score functions can rival complex ones when leveraging reconstruction-based pretext tasks. Reconstruction-based pretext tasks adapt well to various score functions. As such, it holds promising potential for further expansion. Our OOD detection framework, MOODv2, employs the masked image modeling pretext task. Without bells and whistles, MOODv2 impressively enhances 14.30% AUROC to 95.68% on ImageNet and achieves 99.98% on CIFAR-10.
GID: Graph-based Intrusion Detection on Massive Process Traces for Enterprise Security Systems
Intrusion detection system (IDS) is an important part of enterprise security system architecture. In particular, anomaly-based IDS has been widely applied to detect abnormal process behaviors that deviate from the majority. However, such abnormal behavior usually consists of a series of low-level heterogeneous events. The gap between the low-level events and the high-level abnormal behaviors makes it hard to infer which single events are related to the real abnormal activities, especially considering that there are massive "noisy" low-level events happening in between. Hence, the existing work that focus on detecting single entities/events can hardly achieve high detection accuracy. Different from previous work, we design and implement GID, an efficient graph-based intrusion detection technique that can identify abnormal event sequences from a massive heterogeneous process traces with high accuracy. GID first builds a compact graph structure to capture the interactions between different system entities. The suspiciousness or anomaly score of process paths is then measured by leveraging random walk technique to the constructed acyclic directed graph. To eliminate the score bias from the path length, the Box-Cox power transformation based approach is introduced to normalize the anomaly scores so that the scores of paths of different lengths have the same distribution. The efficiency of suspicious path discovery is further improved by the proposed optimization scheme. We fully implement our GID algorithm and deploy it into a real enterprise security system, and it greatly helps detect the advanced threats, and optimize the incident response. Executing GID on system monitoring datasets showing that GID is efficient (about 2 million records per minute) and accurate (higher than 80% in terms of detection rate).
Mean-Shifted Contrastive Loss for Anomaly Detection
Deep anomaly detection methods learn representations that separate between normal and anomalous images. Although self-supervised representation learning is commonly used, small dataset sizes limit its effectiveness. It was previously shown that utilizing external, generic datasets (e.g. ImageNet classification) can significantly improve anomaly detection performance. One approach is outlier exposure, which fails when the external datasets do not resemble the anomalies. We take the approach of transferring representations pre-trained on external datasets for anomaly detection. Anomaly detection performance can be significantly improved by fine-tuning the pre-trained representations on the normal training images. In this paper, we first demonstrate and analyze that contrastive learning, the most popular self-supervised learning paradigm cannot be naively applied to pre-trained features. The reason is that pre-trained feature initialization causes poor conditioning for standard contrastive objectives, resulting in bad optimization dynamics. Based on our analysis, we provide a modified contrastive objective, the Mean-Shifted Contrastive Loss. Our method is highly effective and achieves a new state-of-the-art anomaly detection performance including 98.6% ROC-AUC on the CIFAR-10 dataset.
MedIAnomaly: A comparative study of anomaly detection in medical images
Anomaly detection (AD) aims at detecting abnormal samples that deviate from the expected normal patterns. Generally, it can be trained merely on normal data, without a requirement for abnormal samples, and thereby plays an important role in rare disease recognition and health screening in the medical domain. Despite the emergence of numerous methods for medical AD, the lack of a fair and comprehensive evaluation causes ambiguous conclusions and hinders the development of this field. To address this problem, this paper builds a benchmark with unified comparison. Seven medical datasets with five image modalities, including chest X-rays, brain MRIs, retinal fundus images, dermatoscopic images, and histopathology images, are curated for extensive evaluation. Thirty typical AD methods, including reconstruction and self-supervised learning-based methods, are involved in comparison of image-level anomaly classification and pixel-level anomaly segmentation. Furthermore, for the first time, we systematically investigate the effect of key components in existing methods, revealing unresolved challenges and potential future directions. The datasets and code are available at https://github.com/caiyu6666/MedIAnomaly.
SeaS: Few-shot Industrial Anomaly Image Generation with Separation and Sharing Fine-tuning
We introduce SeaS, a unified industrial generative model for automatically creating diverse anomalies, authentic normal products, and precise anomaly masks. While extensive research exists, most efforts either focus on specific tasks, i.e., anomalies or normal products only, or require separate models for each anomaly type. Consequently, prior methods either offer limited generative capability or depend on a vast array of anomaly-specific models. We demonstrate that U-Net's differentiated learning ability captures the distinct visual traits of slightly-varied normal products and diverse anomalies, enabling us to construct a unified model for all tasks. Specifically, we first introduce an Unbalanced Abnormal (UA) Text Prompt, comprising one normal token and multiple anomaly tokens. More importantly, our Decoupled Anomaly Alignment (DA) loss decouples anomaly attributes and binds them to distinct anomaly tokens of UA, enabling SeaS to create unseen anomalies by recombining these attributes. Furthermore, our Normal-image Alignment (NA) loss aligns the normal token to normal patterns, making generated normal products globally consistent and locally varied. Finally, SeaS produces accurate anomaly masks by fusing discriminative U-Net features with high-resolution VAE features. SeaS sets a new benchmark for industrial generation, significantly enhancing downstream applications, with average improvements of +8.66% pixel-level AP for synthesis-based AD approaches, +1.10% image-level AP for unsupervised AD methods, and +12.79% IoU for supervised segmentation models. Code is available at https://github.com/HUST-SLOW/SeaS{https://github.com/HUST-SLOW/SeaS}.
FiLo: Zero-Shot Anomaly Detection by Fine-Grained Description and High-Quality Localization
Zero-shot anomaly detection (ZSAD) methods entail detecting anomalies directly without access to any known normal or abnormal samples within the target item categories. Existing approaches typically rely on the robust generalization capabilities of multimodal pretrained models, computing similarities between manually crafted textual features representing "normal" or "abnormal" semantics and image features to detect anomalies and localize anomalous patches. However, the generic descriptions of "abnormal" often fail to precisely match diverse types of anomalies across different object categories. Additionally, computing feature similarities for single patches struggles to pinpoint specific locations of anomalies with various sizes and scales. To address these issues, we propose a novel ZSAD method called FiLo, comprising two components: adaptively learned Fine-Grained Description (FG-Des) and position-enhanced High-Quality Localization (HQ-Loc). FG-Des introduces fine-grained anomaly descriptions for each category using Large Language Models (LLMs) and employs adaptively learned textual templates to enhance the accuracy and interpretability of anomaly detection. HQ-Loc, utilizing Grounding DINO for preliminary localization, position-enhanced text prompts, and Multi-scale Multi-shape Cross-modal Interaction (MMCI) module, facilitates more accurate localization of anomalies of different sizes and shapes. Experimental results on datasets like MVTec and VisA demonstrate that FiLo significantly improves the performance of ZSAD in both detection and localization, achieving state-of-the-art performance with an image-level AUC of 83.9% and a pixel-level AUC of 95.9% on the VisA dataset. Code is available at https://github.com/CASIA-IVA-Lab/FiLo.
Denoising Likelihood Score Matching for Conditional Score-based Data Generation
Many existing conditional score-based data generation methods utilize Bayes' theorem to decompose the gradients of a log posterior density into a mixture of scores. These methods facilitate the training procedure of conditional score models, as a mixture of scores can be separately estimated using a score model and a classifier. However, our analysis indicates that the training objectives for the classifier in these methods may lead to a serious score mismatch issue, which corresponds to the situation that the estimated scores deviate from the true ones. Such an issue causes the samples to be misled by the deviated scores during the diffusion process, resulting in a degraded sampling quality. To resolve it, we formulate a novel training objective, called Denoising Likelihood Score Matching (DLSM) loss, for the classifier to match the gradients of the true log likelihood density. Our experimental evidence shows that the proposed method outperforms the previous methods on both Cifar-10 and Cifar-100 benchmarks noticeably in terms of several key evaluation metrics. We thus conclude that, by adopting DLSM, the conditional scores can be accurately modeled, and the effect of the score mismatch issue is alleviated.
Fast kernel methods for Data Quality Monitoring as a goodness-of-fit test
We here propose a machine learning approach for monitoring particle detectors in real-time. The goal is to assess the compatibility of incoming experimental data with a reference dataset, characterising the data behaviour under normal circumstances, via a likelihood-ratio hypothesis test. The model is based on a modern implementation of kernel methods, nonparametric algorithms that can learn any continuous function given enough data. The resulting approach is efficient and agnostic to the type of anomaly that may be present in the data. Our study demonstrates the effectiveness of this strategy on multivariate data from drift tube chamber muon detectors.
Unsupervised Anomaly Detection with Rejection
Anomaly detection aims at detecting unexpected behaviours in the data. Because anomaly detection is usually an unsupervised task, traditional anomaly detectors learn a decision boundary by employing heuristics based on intuitions, which are hard to verify in practice. This introduces some uncertainty, especially close to the decision boundary, that may reduce the user trust in the detector's predictions. A way to combat this is by allowing the detector to reject examples with high uncertainty (Learning to Reject). This requires employing a confidence metric that captures the distance to the decision boundary and setting a rejection threshold to reject low-confidence predictions. However, selecting a proper metric and setting the rejection threshold without labels are challenging tasks. In this paper, we solve these challenges by setting a constant rejection threshold on the stability metric computed by ExCeeD. Our insight relies on a theoretical analysis of such a metric. Moreover, setting a constant threshold results in strong guarantees: we estimate the test rejection rate, and derive a theoretical upper bound for both the rejection rate and the expected prediction cost. Experimentally, we show that our method outperforms some metric-based methods.
Regions of Reliability in the Evaluation of Multivariate Probabilistic Forecasts
Multivariate probabilistic time series forecasts are commonly evaluated via proper scoring rules, i.e., functions that are minimal in expectation for the ground-truth distribution. However, this property is not sufficient to guarantee good discrimination in the non-asymptotic regime. In this paper, we provide the first systematic finite-sample study of proper scoring rules for time-series forecasting evaluation. Through a power analysis, we identify the "region of reliability" of a scoring rule, i.e., the set of practical conditions where it can be relied on to identify forecasting errors. We carry out our analysis on a comprehensive synthetic benchmark, specifically designed to test several key discrepancies between ground-truth and forecast distributions, and we gauge the generalizability of our findings to real-world tasks with an application to an electricity production problem. Our results reveal critical shortcomings in the evaluation of multivariate probabilistic forecasts as commonly performed in the literature.
Improving Autoencoder-based Outlier Detection with Adjustable Probabilistic Reconstruction Error and Mean-shift Outlier Scoring
Autoencoders were widely used in many machine learning tasks thanks to their strong learning ability which has drawn great interest among researchers in the field of outlier detection. However, conventional autoencoder-based methods lacked considerations in two aspects. This limited their performance in outlier detection. First, the mean squared error used in conventional autoencoders ignored the judgment uncertainty of the autoencoder, which limited their representation ability. Second, autoencoders suffered from the abnormal reconstruction problem: some outliers can be unexpectedly reconstructed well, making them difficult to identify from the inliers. To mitigate the aforementioned issues, two novel methods were proposed in this paper. First, a novel loss function named Probabilistic Reconstruction Error (PRE) was constructed to factor in both reconstruction bias and judgment uncertainty. To further control the trade-off of these two factors, two weights were introduced in PRE producing Adjustable Probabilistic Reconstruction Error (APRE), which benefited the outlier detection in different applications. Second, a conceptually new outlier scoring method based on mean-shift (MSS) was proposed to reduce the false inliers caused by the autoencoder. Experiments on 32 real-world outlier detection datasets proved the effectiveness of the proposed methods. The combination of the proposed methods achieved 41% of the relative performance improvement compared to the best baseline. The MSS improved the performance of multiple autoencoder-based outlier detectors by an average of 20%. The proposed two methods have the potential to advance autoencoder's development in outlier detection. The code is available on www.OutlierNet.com for reproducibility.
Mixture of Experts Guided by Gaussian Splatters Matters: A new Approach to Weakly-Supervised Video Anomaly Detection
Video Anomaly Detection (VAD) is a challenging task due to the variability of anomalous events and the limited availability of labeled data. Under the Weakly-Supervised VAD (WSVAD) paradigm, only video-level labels are provided during training, while predictions are made at the frame level. Although state-of-the-art models perform well on simple anomalies (e.g., explosions), they struggle with complex real-world events (e.g., shoplifting). This difficulty stems from two key issues: (1) the inability of current models to address the diversity of anomaly types, as they process all categories with a shared model, overlooking category-specific features; and (2) the weak supervision signal, which lacks precise temporal information, limiting the ability to capture nuanced anomalous patterns blended with normal events. To address these challenges, we propose Gaussian Splatting-guided Mixture of Experts (GS-MoE), a novel framework that employs a set of expert models, each specialized in capturing specific anomaly types. These experts are guided by a temporal Gaussian splatting loss, enabling the model to leverage temporal consistency and enhance weak supervision. The Gaussian splatting approach encourages a more precise and comprehensive representation of anomalies by focusing on temporal segments most likely to contain abnormal events. The predictions from these specialized experts are integrated through a mixture-of-experts mechanism to model complex relationships across diverse anomaly patterns. Our approach achieves state-of-the-art performance, with a 91.58% AUC on the UCF-Crime dataset, and demonstrates superior results on XD-Violence and MSAD datasets. By leveraging category-specific expertise and temporal guidance, GS-MoE sets a new benchmark for VAD under weak supervision.
Exploring Intrinsic Normal Prototypes within a Single Image for Universal Anomaly Detection
Anomaly detection (AD) is essential for industrial inspection, yet existing methods typically rely on ``comparing'' test images to normal references from a training set. However, variations in appearance and positioning often complicate the alignment of these references with the test image, limiting detection accuracy. We observe that most anomalies manifest as local variations, meaning that even within anomalous images, valuable normal information remains. We argue that this information is useful and may be more aligned with the anomalies since both the anomalies and the normal information originate from the same image. Therefore, rather than relying on external normality from the training set, we propose INP-Former, a novel method that extracts Intrinsic Normal Prototypes (INPs) directly from the test image. Specifically, we introduce the INP Extractor, which linearly combines normal tokens to represent INPs. We further propose an INP Coherence Loss to ensure INPs can faithfully represent normality for the testing image. These INPs then guide the INP-Guided Decoder to reconstruct only normal tokens, with reconstruction errors serving as anomaly scores. Additionally, we propose a Soft Mining Loss to prioritize hard-to-optimize samples during training. INP-Former achieves state-of-the-art performance in single-class, multi-class, and few-shot AD tasks across MVTec-AD, VisA, and Real-IAD, positioning it as a versatile and universal solution for AD. Remarkably, INP-Former also demonstrates some zero-shot AD capability. Code is available at:https://github.com/luow23/INP-Former.
Anomaly Detection in Video Using Predictive Convolutional Long Short-Term Memory Networks
Automating the detection of anomalous events within long video sequences is challenging due to the ambiguity of how such events are defined. We approach the problem by learning generative models that can identify anomalies in videos using limited supervision. We propose end-to-end trainable composite Convolutional Long Short-Term Memory (Conv-LSTM) networks that are able to predict the evolution of a video sequence from a small number of input frames. Regularity scores are derived from the reconstruction errors of a set of predictions with abnormal video sequences yielding lower regularity scores as they diverge further from the actual sequence over time. The models utilize a composite structure and examine the effects of conditioning in learning more meaningful representations. The best model is chosen based on the reconstruction and prediction accuracy. The Conv-LSTM models are evaluated both qualitatively and quantitatively, demonstrating competitive results on anomaly detection datasets. Conv-LSTM units are shown to be an effective tool for modeling and predicting video sequences.
Rayleigh Quotient Graph Neural Networks for Graph-level Anomaly Detection
Graph-level anomaly detection has gained significant attention as it finds applications in various domains, such as cancer diagnosis and enzyme prediction. However, existing methods fail to capture the spectral properties of graph anomalies, resulting in unexplainable framework design and unsatisfying performance. In this paper, we re-investigate the spectral differences between anomalous and normal graphs. Our main observation shows a significant disparity in the accumulated spectral energy between these two classes. Moreover, we prove that the accumulated spectral energy of the graph signal can be represented by its Rayleigh Quotient, indicating that the Rayleigh Quotient is a driving factor behind the anomalous properties of graphs. Motivated by this, we propose Rayleigh Quotient Graph Neural Network (RQGNN), the first spectral GNN that explores the inherent spectral features of anomalous graphs for graph-level anomaly detection. Specifically, we introduce a novel framework with two components: the Rayleigh Quotient learning component (RQL) and Chebyshev Wavelet GNN with RQ-pooling (CWGNN-RQ). RQL explicitly captures the Rayleigh Quotient of graphs and CWGNN-RQ implicitly explores the spectral space of graphs. Extensive experiments on 10 real-world datasets show that RQGNN outperforms the best rival by 6.74% in Macro-F1 score and 1.44% in AUC, demonstrating the effectiveness of our framework. Our code is available at https://github.com/xydong127/RQGNN.
Closed-Form Diffusion Models
Score-based generative models (SGMs) sample from a target distribution by iteratively transforming noise using the score function of the perturbed target. For any finite training set, this score function can be evaluated in closed form, but the resulting SGM memorizes its training data and does not generate novel samples. In practice, one approximates the score by training a neural network via score-matching. The error in this approximation promotes generalization, but neural SGMs are costly to train and sample, and the effective regularization this error provides is not well-understood theoretically. In this work, we instead explicitly smooth the closed-form score to obtain an SGM that generates novel samples without training. We analyze our model and propose an efficient nearest-neighbor-based estimator of its score function. Using this estimator, our method achieves competitive sampling times while running on consumer-grade CPUs.
Comparative Evaluation of Anomaly Detection Methods for Fraud Detection in Online Credit Card Payments
This study explores the application of anomaly detection (AD) methods in imbalanced learning tasks, focusing on fraud detection using real online credit card payment data. We assess the performance of several recent AD methods and compare their effectiveness against standard supervised learning methods. Offering evidence of distribution shift within our dataset, we analyze its impact on the tested models' performances. Our findings reveal that LightGBM exhibits significantly superior performance across all evaluated metrics but suffers more from distribution shifts than AD methods. Furthermore, our investigation reveals that LightGBM also captures the majority of frauds detected by AD methods. This observation challenges the potential benefits of ensemble methods to combine supervised, and AD approaches to enhance performance. In summary, this research provides practical insights into the utility of these techniques in real-world scenarios, showing LightGBM's superiority in fraud detection while highlighting challenges related to distribution shifts.
THEMIS: Unlocking Pretrained Knowledge with Foundation Model Embeddings for Anomaly Detection in Time Series
Time series anomaly detection forms a very crucial area in several domains but poses substantial challenges. Due to time series data possessing seasonality, trends, noise, and evolving patterns (concept drift), it becomes very difficult to set a general notion of what constitutes normal behavior. Anomalies themselves could be varied, ranging from a single outlier to contextual or collective anomalies, and are normally very rare; hence, the dataset is largely imbalanced. Additional layers of complexities arise due to the problems of increased dimensionality of modern time series, real-time detection criteria, setting up appropriate detection thresholds, and arriving at results that are interpretable. To embrace these multifaceted challenges, very strong, flexible, and interpretable approaches are required. This paper presents THEMIS, a new framework for time series anomaly detection that exploits pretrained knowledge from foundation models. THEMIS extracts embeddings from the encoder of the Chronos time series foundation model and applies outlier detection techniques like Local Outlier Factor and Spectral Decomposition on the self-similarity matrix, to spot anomalies in the data. Our experiments show that this modular method achieves SOTA results on the MSL dataset and performs quite competitively on the SMAP and SWAT^* datasets. Notably, THEMIS exceeds models trained specifically for anomaly detection, presenting hyperparameter robustness and interpretability by default. This paper advocates for pretrained representations from foundation models for performing efficient and adaptable anomaly detection for time series data.
Text-ADBench: Text Anomaly Detection Benchmark based on LLMs Embedding
Text anomaly detection is a critical task in natural language processing (NLP), with applications spanning fraud detection, misinformation identification, spam detection and content moderation, etc. Despite significant advances in large language models (LLMs) and anomaly detection algorithms, the absence of standardized and comprehensive benchmarks for evaluating the existing anomaly detection methods on text data limits rigorous comparison and development of innovative approaches. This work performs a comprehensive empirical study and introduces a benchmark for text anomaly detection, leveraging embeddings from diverse pre-trained language models across a wide array of text datasets. Our work systematically evaluates the effectiveness of embedding-based text anomaly detection by incorporating (1) early language models (GloVe, BERT); (2) multiple LLMs (LLaMa-2, LLama-3, Mistral, OpenAI (small, ada, large)); (3) multi-domain text datasets (news, social media, scientific publications); (4) comprehensive evaluation metrics (AUROC, AUPRC). Our experiments reveal a critical empirical insight: embedding quality significantly governs anomaly detection efficacy, and deep learning-based approaches demonstrate no performance advantage over conventional shallow algorithms (e.g., KNN, Isolation Forest) when leveraging LLM-derived embeddings.In addition, we observe strongly low-rank characteristics in cross-model performance matrices, which enables an efficient strategy for rapid model evaluation (or embedding evaluation) and selection in practical applications. Furthermore, by open-sourcing our benchmark toolkit that includes all embeddings from different models and code at https://github.com/jicongfan/Text-Anomaly-Detection-Benchmark, this work provides a foundation for future research in robust and scalable text anomaly detection systems.
Using Machine Learning for Anomaly Detection on a System-on-Chip under Gamma Radiation
The emergence of new nanoscale technologies has imposed significant challenges to designing reliable electronic systems in radiation environments. A few types of radiation like Total Ionizing Dose (TID) effects often cause permanent damages on such nanoscale electronic devices, and current state-of-the-art technologies to tackle TID make use of expensive radiation-hardened devices. This paper focuses on a novel and different approach: using machine learning algorithms on consumer electronic level Field Programmable Gate Arrays (FPGAs) to tackle TID effects and monitor them to replace before they stop working. This condition has a research challenge to anticipate when the board results in a total failure due to TID effects. We observed internal measurements of the FPGA boards under gamma radiation and used three different anomaly detection machine learning (ML) algorithms to detect anomalies in the sensor measurements in a gamma-radiated environment. The statistical results show a highly significant relationship between the gamma radiation exposure levels and the board measurements. Moreover, our anomaly detection results have shown that a One-Class Support Vector Machine with Radial Basis Function Kernel has an average Recall score of 0.95. Also, all anomalies can be detected before the boards stop working.
Few-Shot Anomaly-Driven Generation for Anomaly Classification and Segmentation
Anomaly detection is a practical and challenging task due to the scarcity of anomaly samples in industrial inspection. Some existing anomaly detection methods address this issue by synthesizing anomalies with noise or external data. However, there is always a large semantic gap between synthetic and real-world anomalies, resulting in weak performance in anomaly detection. To solve the problem, we propose a few-shot Anomaly-driven Generation (AnoGen) method, which guides the diffusion model to generate realistic and diverse anomalies with only a few real anomalies, thereby benefiting training anomaly detection models. Specifically, our work is divided into three stages. In the first stage, we learn the anomaly distribution based on a few given real anomalies and inject the learned knowledge into an embedding. In the second stage, we use the embedding and given bounding boxes to guide the diffusion model to generate realistic and diverse anomalies on specific objects (or textures). In the final stage, we propose a weakly-supervised anomaly detection method to train a more powerful model with generated anomalies. Our method builds upon DRAEM and DesTSeg as the foundation model and conducts experiments on the commonly used industrial anomaly detection dataset, MVTec. The experiments demonstrate that our generated anomalies effectively improve the model performance of both anomaly classification and segmentation tasks simultaneously, \eg, DRAEM and DseTSeg achieved a 5.8\% and 1.5\% improvement in AU-PR metric on segmentation task, respectively. The code and generated anomalous data are available at https://github.com/gaobb/AnoGen.
Detecting Adversarial Data by Probing Multiple Perturbations Using Expected Perturbation Score
Adversarial detection aims to determine whether a given sample is an adversarial one based on the discrepancy between natural and adversarial distributions. Unfortunately, estimating or comparing two data distributions is extremely difficult, especially in high-dimension spaces. Recently, the gradient of log probability density (a.k.a., score) w.r.t. the sample is used as an alternative statistic to compute. However, we find that the score is sensitive in identifying adversarial samples due to insufficient information with one sample only. In this paper, we propose a new statistic called expected perturbation score (EPS), which is essentially the expected score of a sample after various perturbations. Specifically, to obtain adequate information regarding one sample, we perturb it by adding various noises to capture its multi-view observations. We theoretically prove that EPS is a proper statistic to compute the discrepancy between two samples under mild conditions. In practice, we can use a pre-trained diffusion model to estimate EPS for each sample. Last, we propose an EPS-based adversarial detection (EPS-AD) method, in which we develop EPS-based maximum mean discrepancy (MMD) as a metric to measure the discrepancy between the test sample and natural samples. We also prove that the EPS-based MMD between natural and adversarial samples is larger than that among natural samples. Extensive experiments show the superior adversarial detection performance of our EPS-AD.
Unilaterally Aggregated Contrastive Learning with Hierarchical Augmentation for Anomaly Detection
Anomaly detection (AD), aiming to find samples that deviate from the training distribution, is essential in safety-critical applications. Though recent self-supervised learning based attempts achieve promising results by creating virtual outliers, their training objectives are less faithful to AD which requires a concentrated inlier distribution as well as a dispersive outlier distribution. In this paper, we propose Unilaterally Aggregated Contrastive Learning with Hierarchical Augmentation (UniCon-HA), taking into account both the requirements above. Specifically, we explicitly encourage the concentration of inliers and the dispersion of virtual outliers via supervised and unsupervised contrastive losses, respectively. Considering that standard contrastive data augmentation for generating positive views may induce outliers, we additionally introduce a soft mechanism to re-weight each augmented inlier according to its deviation from the inlier distribution, to ensure a purified concentration. Moreover, to prompt a higher concentration, inspired by curriculum learning, we adopt an easy-to-hard hierarchical augmentation strategy and perform contrastive aggregation at different depths of the network based on the strengths of data augmentation. Our method is evaluated under three AD settings including unlabeled one-class, unlabeled multi-class, and labeled multi-class, demonstrating its consistent superiority over other competitors.
Learning Optimized Risk Scores
Risk scores are simple classification models that let users make quick risk predictions by adding and subtracting a few small numbers. These models are widely used in medicine and criminal justice, but are difficult to learn from data because they need to be calibrated, sparse, use small integer coefficients, and obey application-specific operational constraints. In this paper, we present a new machine learning approach to learn risk scores. We formulate the risk score problem as a mixed integer nonlinear program, and present a cutting plane algorithm for non-convex settings to efficiently recover its optimal solution. We improve our algorithm with specialized techniques to generate feasible solutions, narrow the optimality gap, and reduce data-related computation. Our approach can fit risk scores in a way that scales linearly in the number of samples, provides a certificate of optimality, and obeys real-world constraints without parameter tuning or post-processing. We benchmark the performance benefits of this approach through an extensive set of numerical experiments, comparing to risk scores built using heuristic approaches. We also discuss its practical benefits through a real-world application where we build a customized risk score for ICU seizure prediction in collaboration with the Massachusetts General Hospital.
Follow the Rules: Reasoning for Video Anomaly Detection with Large Language Models
Video Anomaly Detection (VAD) is crucial for applications such as security surveillance and autonomous driving. However, existing VAD methods provide little rationale behind detection, hindering public trust in real-world deployments. In this paper, we approach VAD with a reasoning framework. Although Large Language Models (LLMs) have shown revolutionary reasoning ability, we find that their direct use falls short of VAD. Specifically, the implicit knowledge pre-trained in LLMs focuses on general context and thus may not apply to every specific real-world VAD scenario, leading to inflexibility and inaccuracy. To address this, we propose AnomalyRuler, a novel rule-based reasoning framework for VAD with LLMs. AnomalyRuler comprises two main stages: induction and deduction. In the induction stage, the LLM is fed with few-shot normal reference samples and then summarizes these normal patterns to induce a set of rules for detecting anomalies. The deduction stage follows the induced rules to spot anomalous frames in test videos. Additionally, we design rule aggregation, perception smoothing, and robust reasoning strategies to further enhance AnomalyRuler's robustness. AnomalyRuler is the first reasoning approach for the one-class VAD task, which requires only few-normal-shot prompting without the need for full-shot training, thereby enabling fast adaption to various VAD scenarios. Comprehensive experiments across four VAD benchmarks demonstrate AnomalyRuler's state-of-the-art detection performance and reasoning ability. AnomalyRuler is open-source and available at: https://github.com/Yuchen413/AnomalyRuler
Robust Evaluation Measures for Evaluating Social Biases in Masked Language Models
Many evaluation measures are used to evaluate social biases in masked language models (MLMs). However, we find that these previously proposed evaluation measures are lacking robustness in scenarios with limited datasets. This is because these measures are obtained by comparing the pseudo-log-likelihood (PLL) scores of the stereotypical and anti-stereotypical samples using an indicator function. The disadvantage is the limited mining of the PLL score sets without capturing its distributional information. In this paper, we represent a PLL score set as a Gaussian distribution and use Kullback Leibler (KL) divergence and Jensen Shannon (JS) divergence to construct evaluation measures for the distributions of stereotypical and anti-stereotypical PLL scores. Experimental results on the publicly available datasets StereoSet (SS) and CrowS-Pairs (CP) show that our proposed measures are significantly more robust and interpretable than those proposed previously.
Approximate Stein Classes for Truncated Density Estimation
Estimating truncated density models is difficult, as these models have intractable normalising constants and hard to satisfy boundary conditions. Score matching can be adapted to solve the truncated density estimation problem, but requires a continuous weighting function which takes zero at the boundary and is positive elsewhere. Evaluation of such a weighting function (and its gradient) often requires a closed-form expression of the truncation boundary and finding a solution to a complicated optimisation problem. In this paper, we propose approximate Stein classes, which in turn leads to a relaxed Stein identity for truncated density estimation. We develop a novel discrepancy measure, truncated kernelised Stein discrepancy (TKSD), which does not require fixing a weighting function in advance, and can be evaluated using only samples on the boundary. We estimate a truncated density model by minimising the Lagrangian dual of TKSD. Finally, experiments show the accuracy of our method to be an improvement over previous works even without the explicit functional form of the boundary.
Feature Shift Detection: Localizing Which Features Have Shifted via Conditional Distribution Tests
While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (i.e. gradient with respect to the input) -- which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models. We additionally develop methods for identifying when and where a shift occurs in multivariate time-series data and show results for multiple scenarios using realistic attack models on both simulated and real world data.
CT-AGRG: Automated Abnormality-Guided Report Generation from 3D Chest CT Volumes
The rapid increase of computed tomography (CT) scans and their time-consuming manual analysis have created an urgent need for robust automated analysis techniques in clinical settings. These aim to assist radiologists and help them managing their growing workload. Existing methods typically generate entire reports directly from 3D CT images, without explicitly focusing on observed abnormalities. This unguided approach often results in repetitive content or incomplete reports, failing to prioritize anomaly-specific descriptions. We propose a new anomaly-guided report generation model, which first predicts abnormalities and then generates targeted descriptions for each. Evaluation on a public dataset demonstrates significant improvements in report quality and clinical relevance. We extend our work by conducting an ablation study to demonstrate its effectiveness.
Fascinating Supervisory Signals and Where to Find Them: Deep Anomaly Detection with Scale Learning
Due to the unsupervised nature of anomaly detection, the key to fueling deep models is finding supervisory signals. Different from current reconstruction-guided generative models and transformation-based contrastive models, we devise novel data-driven supervision for tabular data by introducing a characteristic -- scale -- as data labels. By representing varied sub-vectors of data instances, we define scale as the relationship between the dimensionality of original sub-vectors and that of representations. Scales serve as labels attached to transformed representations, thus offering ample labeled data for neural network training. This paper further proposes a scale learning-based anomaly detection method. Supervised by the learning objective of scale distribution alignment, our approach learns the ranking of representations converted from varied subspaces of each data instance. Through this proxy task, our approach models inherent regularities and patterns within data, which well describes data "normality". Abnormal degrees of testing instances are obtained by measuring whether they fit these learned patterns. Extensive experiments show that our approach leads to significant improvement over state-of-the-art generative/contrastive anomaly detection methods.
AES Systems Are Both Overstable And Oversensitive: Explaining Why And Proposing Defenses
Deep-learning based Automatic Essay Scoring (AES) systems are being actively used by states and language testing agencies alike to evaluate millions of candidates for life-changing decisions ranging from college applications to visa approvals. However, little research has been put to understand and interpret the black-box nature of deep-learning based scoring algorithms. Previous studies indicate that scoring models can be easily fooled. In this paper, we explore the reason behind their surprising adversarial brittleness. We utilize recent advances in interpretability to find the extent to which features such as coherence, content, vocabulary, and relevance are important for automated scoring mechanisms. We use this to investigate the oversensitivity i.e., large change in output score with a little change in input essay content) and overstability i.e., little change in output scores with large changes in input essay content) of AES. Our results indicate that autoscoring models, despite getting trained as "end-to-end" models with rich contextual embeddings such as BERT, behave like bag-of-words models. A few words determine the essay score without the requirement of any context making the model largely overstable. This is in stark contrast to recent probing studies on pre-trained representation learning models, which show that rich linguistic features such as parts-of-speech and morphology are encoded by them. Further, we also find that the models have learnt dataset biases, making them oversensitive. To deal with these issues, we propose detection-based protection models that can detect oversensitivity and overstability causing samples with high accuracies. We find that our proposed models are able to detect unusual attribution patterns and flag adversarial samples successfully.
Structured Temporal Causality for Interpretable Multivariate Time Series Anomaly Detection
Real-world multivariate time series anomalies are rare and often unlabeled. Additionally, prevailing methods rely on increasingly complex architectures tuned to benchmarks, detecting only fragments of anomalous segments and overstating performance. In this paper, we introduce OracleAD, a simple and interpretable unsupervised framework for multivariate time series anomaly detection. OracleAD encodes each variable's past sequence into a single causal embedding to jointly predict the present time point and reconstruct the input window, effectively modeling temporal dynamics. These embeddings then undergo a self-attention mechanism to project them into a shared latent space and capture spatial relationships. These relationships are not static, since they are modeled by a property that emerges from each variable's temporal dynamics. The projected embeddings are aligned to a Stable Latent Structure (SLS) representing normal-state relationships. Anomalies are identified using a dual scoring mechanism based on prediction error and deviation from the SLS, enabling fine-grained anomaly diagnosis at each time point and across individual variables. Since any noticeable SLS deviation originates from embeddings that violate the learned temporal causality of normal data, OracleAD directly pinpoints the root-cause variables at the embedding level. OracleAD achieves state-of-the-art results across multiple real-world datasets and evaluation protocols, while remaining interpretable through SLS.
UGainS: Uncertainty Guided Anomaly Instance Segmentation
A single unexpected object on the road can cause an accident or may lead to injuries. To prevent this, we need a reliable mechanism for finding anomalous objects on the road. This task, called anomaly segmentation, can be a stepping stone to safe and reliable autonomous driving. Current approaches tackle anomaly segmentation by assigning an anomaly score to each pixel and by grouping anomalous regions using simple heuristics. However, pixel grouping is a limiting factor when it comes to evaluating the segmentation performance of individual anomalous objects. To address the issue of grouping multiple anomaly instances into one, we propose an approach that produces accurate anomaly instance masks. Our approach centers on an out-of-distribution segmentation model for identifying uncertain regions and a strong generalist segmentation model for anomaly instances segmentation. We investigate ways to use uncertain regions to guide such a segmentation model to perform segmentation of anomalous instances. By incorporating strong object priors from a generalist model we additionally improve the per-pixel anomaly segmentation performance. Our approach outperforms current pixel-level anomaly segmentation methods, achieving an AP of 80.08% and 88.98% on the Fishyscapes Lost and Found and the RoadAnomaly validation sets respectively. Project page: https://vision.rwth-aachen.de/ugains
Language-Assisted Feature Transformation for Anomaly Detection
This paper introduces LAFT, a novel feature transformation method designed to incorporate user knowledge and preferences into anomaly detection using natural language. Accurately modeling the boundary of normality is crucial for distinguishing abnormal data, but this is often challenging due to limited data or the presence of nuisance attributes. While unsupervised methods that rely solely on data without user guidance are common, they may fail to detect anomalies of specific interest. To address this limitation, we propose Language-Assisted Feature Transformation (LAFT), which leverages the shared image-text embedding space of vision-language models to transform visual features according to user-defined requirements. Combined with anomaly detection methods, LAFT effectively aligns visual features with user preferences, allowing anomalies of interest to be detected. Extensive experiments on both toy and real-world datasets validate the effectiveness of our method.
What If the Input is Expanded in OOD Detection?
Out-of-distribution (OOD) detection aims to identify OOD inputs from unknown classes, which is important for the reliable deployment of machine learning models in the open world. Various scoring functions are proposed to distinguish it from in-distribution (ID) data. However, existing methods generally focus on excavating the discriminative information from a single input, which implicitly limits its representation dimension. In this work, we introduce a novel perspective, i.e., employing different common corruptions on the input space, to expand that. We reveal an interesting phenomenon termed confidence mutation, where the confidence of OOD data can decrease significantly under the corruptions, while the ID data shows a higher confidence expectation considering the resistance of semantic features. Based on that, we formalize a new scoring method, namely, Confidence aVerage (CoVer), which can capture the dynamic differences by simply averaging the scores obtained from different corrupted inputs and the original ones, making the OOD and ID distributions more separable in detection tasks. Extensive experiments and analyses have been conducted to understand and verify the effectiveness of CoVer. The code is publicly available at: https://github.com/tmlr-group/CoVer.
AnomalyNCD: Towards Novel Anomaly Class Discovery in Industrial Scenarios
Recently, multi-class anomaly classification has garnered increasing attention. Previous methods directly cluster anomalies but often struggle due to the lack of anomaly-prior knowledge. Acquiring this knowledge faces two issues: the non-prominent and weak-semantics anomalies. In this paper, we propose AnomalyNCD, a multi-class anomaly classification network compatible with different anomaly detection methods. To address the non-prominence of anomalies, we design main element binarization (MEBin) to obtain anomaly-centered images, ensuring anomalies are learned while avoiding the impact of incorrect detections. Next, to learn anomalies with weak semantics, we design mask-guided representation learning, which focuses on isolated anomalies guided by masks and reduces confusion from erroneous inputs through corrected pseudo labels. Finally, to enable flexible classification at both region and image levels, we develop a region merging strategy that determines the overall image category based on the classified anomaly regions. Our method outperforms the state-of-the-art works on the MVTec AD and MTD datasets. Compared with the current methods, AnomalyNCD combined with zero-shot anomaly detection method achieves a 10.8% F_1 gain, 8.8% NMI gain, and 9.5% ARI gain on MVTec AD, and 12.8% F_1 gain, 5.7% NMI gain, and 10.8% ARI gain on MTD. Code is available at https://github.com/HUST-SLOW/AnomalyNCD.
AnomalyGPT: Detecting Industrial Anomalies using Large Vision-Language Models
Large Vision-Language Models (LVLMs) such as MiniGPT-4 and LLaVA have demonstrated the capability of understanding images and achieved remarkable performance in various visual tasks. Despite their strong abilities in recognizing common objects due to extensive training datasets, they lack specific domain knowledge and have a weaker understanding of localized details within objects, which hinders their effectiveness in the Industrial Anomaly Detection (IAD) task. On the other hand, most existing IAD methods only provide anomaly scores and necessitate the manual setting of thresholds to distinguish between normal and abnormal samples, which restricts their practical implementation. In this paper, we explore the utilization of LVLM to address the IAD problem and propose AnomalyGPT, a novel IAD approach based on LVLM. We generate training data by simulating anomalous images and producing corresponding textual descriptions for each image. We also employ an image decoder to provide fine-grained semantic and design a prompt learner to fine-tune the LVLM using prompt embeddings. Our AnomalyGPT eliminates the need for manual threshold adjustments, thus directly assesses the presence and locations of anomalies. Additionally, AnomalyGPT supports multi-turn dialogues and exhibits impressive few-shot in-context learning capabilities. With only one normal shot, AnomalyGPT achieves the state-of-the-art performance with an accuracy of 86.1%, an image-level AUC of 94.1%, and a pixel-level AUC of 95.3% on the MVTec-AD dataset. Code is available at https://github.com/CASIA-IVA-Lab/AnomalyGPT.
Dimensionless Anomaly Detection on Multivariate Streams with Variance Norm and Path Signature
In this paper, we propose a dimensionless anomaly detection method for multivariate streams. Our method is independent of the unit of measurement for the different stream channels, therefore dimensionless. We first propose the variance norm, a generalisation of Mahalanobis distance to handle infinite-dimensional feature space and singular empirical covariance matrix rigorously. We then combine the variance norm with the path signature, an infinite collection of iterated integrals that provide global features of streams, to propose SigMahaKNN, a method for anomaly detection on (multivariate) streams. We show that SigMahaKNN is invariant to stream reparametrisation, stream concatenation and has a graded discrimination power depending on the truncation level of the path signature. We implement SigMahaKNN as an open-source software, and perform extensive numerical experiments, showing significantly improved anomaly detection on streams compared to isolation forest and local outlier factors in applications ranging from language analysis, hand-writing analysis, ship movement paths analysis and univariate time-series analysis.
The Unreasonable Effectiveness of Gaussian Score Approximation for Diffusion Models and its Applications
By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates to the score of the underlying data manifold remains largely unclear. Here, we aim to elucidate this relationship by comparing learned neural scores to the scores of two kinds of analytically tractable distributions: Gaussians and Gaussian mixtures. The simplicity of the Gaussian model makes it theoretically attractive, and we show that it admits a closed-form solution and predicts many qualitative aspects of sample generation dynamics. We claim that the learned neural score is dominated by its linear (Gaussian) approximation for moderate to high noise scales, and supply both theoretical and empirical arguments to support this claim. Moreover, the Gaussian approximation empirically works for a larger range of noise scales than naive theory suggests it should, and is preferentially learned early in training. At smaller noise scales, we observe that learned scores are better described by a coarse-grained (Gaussian mixture) approximation of training data than by the score of the training distribution, a finding consistent with generalization. Our findings enable us to precisely predict the initial phase of trained models' sampling trajectories through their Gaussian approximations. We show that this allows the skipping of the first 15-30% of sampling steps while maintaining high sample quality (with a near state-of-the-art FID score of 1.93 on CIFAR-10 unconditional generation). This forms the foundation of a novel hybrid sampling method, termed analytical teleportation, which can seamlessly integrate with and accelerate existing samplers, including DPM-Solver-v3 and UniPC. Our findings suggest ways to improve the design and training of diffusion models.
Accurate and robust methods for direct background estimation in resonant anomaly detection
Resonant anomaly detection methods have great potential for enhancing the sensitivity of traditional bump hunt searches. A key component of these methods is a high quality background template used to produce an anomaly score. Using the LHC Olympics R&D dataset, we demonstrate that this background template can also be repurposed to directly estimate the background expectation in a simple cut and count setup. In contrast to a traditional bump hunt, no fit to the invariant mass distribution is needed, thereby avoiding the potential problem of background sculpting. Furthermore, direct background estimation allows working with large background rejection rates, where resonant anomaly detection methods typically show their greatest improvement in significance.
MANO: Exploiting Matrix Norm for Unsupervised Accuracy Estimation Under Distribution Shifts
Leveraging the models' outputs, specifically the logits, is a common approach to estimating the test accuracy of a pre-trained neural network on out-of-distribution (OOD) samples without requiring access to the corresponding ground truth labels. Despite their ease of implementation and computational efficiency, current logit-based methods are vulnerable to overconfidence issues, leading to prediction bias, especially under the natural shift. In this work, we first study the relationship between logits and generalization performance from the view of low-density separation assumption. Our findings motivate our proposed method MaNo which (1) applies a data-dependent normalization on the logits to reduce prediction bias, and (2) takes the L_p norm of the matrix of normalized logits as the estimation score. Our theoretical analysis highlights the connection between the provided score and the model's uncertainty. We conduct an extensive empirical study on common unsupervised accuracy estimation benchmarks and demonstrate that MaNo achieves state-of-the-art performance across various architectures in the presence of synthetic, natural, or subpopulation shifts.
Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions
We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small L^2 error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order moment, by either employing early stopping or assuming smoothness condition on the score function of the data distribution. Our result does not rely on any log-concavity or functional inequality assumption and has a logarithmic dependence on the smoothness. In particular, we show that under only a finite second moment condition, approximating the following in reverse KL divergence in epsilon-accuracy can be done in tilde Oleft(d log (1/delta){epsilon}right) steps: 1) the variance-delta Gaussian perturbation of any data distribution; 2) data distributions with 1/delta-smooth score functions. Our analysis also provides a quantitative comparison between different discrete approximations and may guide the choice of discretization points in practice.
AnomalyBERT: Self-Supervised Transformer for Time Series Anomaly Detection using Data Degradation Scheme
Mechanical defects in real situations affect observation values and cause abnormalities in multivariate time series, such as sensor values or network data. To perceive abnormalities in such data, it is crucial to understand the temporal context and interrelation between variables simultaneously. The anomaly detection task for time series, especially for unlabeled data, has been a challenging problem, and we address it by applying a suitable data degradation scheme to self-supervised model training. We define four types of synthetic outliers and propose the degradation scheme in which a portion of input data is replaced with one of the synthetic outliers. Inspired by the self-attention mechanism, we design a Transformer-based architecture to recognize the temporal context and detect unnatural sequences with high efficiency. Our model converts multivariate data points into temporal representations with relative position bias and yields anomaly scores from these representations. Our method, AnomalyBERT, shows a great capability of detecting anomalies contained in complex time series and surpasses previous state-of-the-art methods on five real-world benchmarks. Our code is available at https://github.com/Jhryu30/AnomalyBERT.
Are we certain it's anomalous?
The progress in modelling time series and, more generally, sequences of structured data has recently revamped research in anomaly detection. The task stands for identifying abnormal behaviors in financial series, IT systems, aerospace measurements, and the medical domain, where anomaly detection may aid in isolating cases of depression and attend the elderly. Anomaly detection in time series is a complex task since anomalies are rare due to highly non-linear temporal correlations and since the definition of anomalous is sometimes subjective. Here we propose the novel use of Hyperbolic uncertainty for Anomaly Detection (HypAD). HypAD learns self-supervisedly to reconstruct the input signal. We adopt best practices from the state-of-the-art to encode the sequence by an LSTM, jointly learned with a decoder to reconstruct the signal, with the aid of GAN critics. Uncertainty is estimated end-to-end by means of a hyperbolic neural network. By using uncertainty, HypAD may assess whether it is certain about the input signal but it fails to reconstruct it because this is anomalous; or whether the reconstruction error does not necessarily imply anomaly, as the model is uncertain, e.g. a complex but regular input signal. The novel key idea is that a detectable anomaly is one where the model is certain but it predicts wrongly. HypAD outperforms the current state-of-the-art for univariate anomaly detection on established benchmarks based on data from NASA, Yahoo, Numenta, Amazon, and Twitter. It also yields state-of-the-art performance on a multivariate dataset of anomaly activities in elderly home residences, and it outperforms the baseline on SWaT. Overall, HypAD yields the lowest false alarms at the best performance rate, thanks to successfully identifying detectable anomalies.
Conformal Risk Control
We extend conformal prediction to control the expected value of any monotone loss function. The algorithm generalizes split conformal prediction together with its coverage guarantee. Like conformal prediction, the conformal risk control procedure is tight up to an O(1/n) factor. We also introduce extensions of the idea to distribution shift, quantile risk control, multiple and adversarial risk control, and expectations of U-statistics. Worked examples from computer vision and natural language processing demonstrate the usage of our algorithm to bound the false negative rate, graph distance, and token-level F1-score.
VADER: Towards Causal Video Anomaly Understanding with Relation-Aware Large Language Models
Video anomaly understanding (VAU) aims to provide detailed interpretation and semantic comprehension of anomalous events within videos, addressing limitations of traditional methods that focus solely on detecting and localizing anomalies. However, existing approaches often neglect the deeper causal relationships and interactions between objects, which are critical for understanding anomalous behaviors. In this paper, we propose VADER, an LLM-driven framework for Video Anomaly unDErstanding, which integrates keyframe object Relation features with visual cues to enhance anomaly comprehension from video. Specifically, VADER first applies an Anomaly Scorer to assign per-frame anomaly scores, followed by a Context-AwarE Sampling (CAES) strategy to capture the causal context of each anomalous event. A Relation Feature Extractor and a COntrastive Relation Encoder (CORE) jointly model dynamic object interactions, producing compact relational representations for downstream reasoning. These visual and relational cues are integrated with LLMs to generate detailed, causally grounded descriptions and support robust anomaly-related question answering. Experiments on multiple real-world VAU benchmarks demonstrate that VADER achieves strong results across anomaly description, explanation, and causal reasoning tasks, advancing the frontier of explainable video anomaly analysis.
On Second-Order Scoring Rules for Epistemic Uncertainty Quantification
It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various machine learning methods have recently been developed with the goal to let the learner also represent its epistemic uncertainty, i.e., the uncertainty caused by a lack of knowledge and data. An emerging branch of the literature proposes the use of a second-order learner that provides predictions in terms of distributions on probability distributions. However, recent work has revealed serious theoretical shortcomings for second-order predictors based on loss minimisation. In this paper, we generalise these findings and prove a more fundamental result: There seems to be no loss function that provides an incentive for a second-order learner to faithfully represent its epistemic uncertainty in the same manner as proper scoring rules do for standard (first-order) learners. As a main mathematical tool to prove this result, we introduce the generalised notion of second-order scoring rules.
Reward Gaming in Conditional Text Generation
To align conditional text generation model outputs with desired behaviors, there has been an increasing focus on training the model using reinforcement learning (RL) with reward functions learned from human annotations. Under this framework, we identify three common cases where high rewards are incorrectly assigned to undesirable patterns: noise-induced spurious correlation, naturally occurring spurious correlation, and covariate shift. We show that even though learned metrics achieve high performance on the distribution of the data used to train the reward function, the undesirable patterns may be amplified during RL training of the text generation model. While there has been discussion about reward gaming in the RL or safety community, in this discussion piece, we would like to highlight reward gaming in the natural language generation (NLG) community using concrete conditional text generation examples and discuss potential fixes and areas for future work.
A Unified Evaluation Framework for Novelty Detection and Accommodation in NLP with an Instantiation in Authorship Attribution
State-of-the-art natural language processing models have been shown to achieve remarkable performance in 'closed-world' settings where all the labels in the evaluation set are known at training time. However, in real-world settings, 'novel' instances that do not belong to any known class are often observed. This renders the ability to deal with novelties crucial. To initiate a systematic research in this important area of 'dealing with novelties', we introduce 'NoveltyTask', a multi-stage task to evaluate a system's performance on pipelined novelty 'detection' and 'accommodation' tasks. We provide mathematical formulation of NoveltyTask and instantiate it with the authorship attribution task that pertains to identifying the correct author of a given text. We use Amazon reviews corpus and compile a large dataset (consisting of 250k instances across 200 authors/labels) for NoveltyTask. We conduct comprehensive experiments and explore several baseline methods for the task. Our results show that the methods achieve considerably low performance making the task challenging and leaving sufficient room for improvement. Finally, we believe our work will encourage research in this underexplored area of dealing with novelties, an important step en route to developing robust systems.
Statistical Learning under Heterogenous Distribution Shift
This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.
A Comprehensive Survey of Regression Based Loss Functions for Time Series Forecasting
Time Series Forecasting has been an active area of research due to its many applications ranging from network usage prediction, resource allocation, anomaly detection, and predictive maintenance. Numerous publications published in the last five years have proposed diverse sets of objective loss functions to address cases such as biased data, long-term forecasting, multicollinear features, etc. In this paper, we have summarized 14 well-known regression loss functions commonly used for time series forecasting and listed out the circumstances where their application can aid in faster and better model convergence. We have also demonstrated how certain categories of loss functions perform well across all data sets and can be considered as a baseline objective function in circumstances where the distribution of the data is unknown. Our code is available at GitHub: https://github.com/aryan-jadon/Regression-Loss-Functions-in-Time-Series-Forecasting-Tensorflow.
RbA: Segmenting Unknown Regions Rejected by All
Standard semantic segmentation models owe their success to curated datasets with a fixed set of semantic categories, without contemplating the possibility of identifying unknown objects from novel categories. Existing methods in outlier detection suffer from a lack of smoothness and objectness in their predictions, due to limitations of the per-pixel classification paradigm. Furthermore, additional training for detecting outliers harms the performance of known classes. In this paper, we explore another paradigm with region-level classification to better segment unknown objects. We show that the object queries in mask classification tend to behave like one \vs all classifiers. Based on this finding, we propose a novel outlier scoring function called RbA by defining the event of being an outlier as being rejected by all known classes. Our extensive experiments show that mask classification improves the performance of the existing outlier detection methods, and the best results are achieved with the proposed RbA. We also propose an objective to optimize RbA using minimal outlier supervision. Further fine-tuning with outliers improves the unknown performance, and unlike previous methods, it does not degrade the inlier performance.
Dive into Time-Series Anomaly Detection: A Decade Review
Recent advances in data collection technology, accompanied by the ever-rising volume and velocity of streaming data, underscore the vital need for time series analytics. In this regard, time-series anomaly detection has been an important activity, entailing various applications in fields such as cyber security, financial markets, law enforcement, and health care. While traditional literature on anomaly detection is centered on statistical measures, the increasing number of machine learning algorithms in recent years call for a structured, general characterization of the research methods for time-series anomaly detection. This survey groups and summarizes anomaly detection existing solutions under a process-centric taxonomy in the time series context. In addition to giving an original categorization of anomaly detection methods, we also perform a meta-analysis of the literature and outline general trends in time-series anomaly detection research.
Magnitude of arithmetic scalar and matrix categories
We develop tools for explicitly constructing categories enriched over generating data and that compose via ordinary scalar and matrix arithmetic arithmetic operations. We characterize meaningful size maps, weightings, and magnitude that reveal features analogous to outliers that these same notions have previously been shown to reveal in the context of metric spaces. Throughout, we provide examples of such "outlier detection" relevant to the analysis of computer programs, neural networks, cyber-physical systems, and networks of communications channels.
Evaluating and Aggregating Feature-based Model Explanations
A feature-based model explanation denotes how much each input feature contributes to a model's output for a given data point. As the number of proposed explanation functions grows, we lack quantitative evaluation criteria to help practitioners know when to use which explanation function. This paper proposes quantitative evaluation criteria for feature-based explanations: low sensitivity, high faithfulness, and low complexity. We devise a framework for aggregating explanation functions. We develop a procedure for learning an aggregate explanation function with lower complexity and then derive a new aggregate Shapley value explanation function that minimizes sensitivity.
InfFeed: Influence Functions as a Feedback to Improve the Performance of Subjective Tasks
Recently, influence functions present an apparatus for achieving explainability for deep neural models by quantifying the perturbation of individual train instances that might impact a test prediction. Our objectives in this paper are twofold. First we incorporate influence functions as a feedback into the model to improve its performance. Second, in a dataset extension exercise, using influence functions to automatically identify data points that have been initially `silver' annotated by some existing method and need to be cross-checked (and corrected) by annotators to improve the model performance. To meet these objectives, in this paper, we introduce InfFeed, which uses influence functions to compute the influential instances for a target instance. Toward the first objective, we adjust the label of the target instance based on its influencer(s) label. In doing this, InfFeed outperforms the state-of-the-art baselines (including LLMs) by a maximum macro F1-score margin of almost 4% for hate speech classification, 3.5% for stance classification, and 3% for irony and 2% for sarcasm detection. Toward the second objective we show that manually re-annotating only those silver annotated data points in the extension set that have a negative influence can immensely improve the model performance bringing it very close to the scenario where all the data points in the extension set have gold labels. This allows for huge reduction of the number of data points that need to be manually annotated since out of the silver annotated extension dataset, the influence function scheme picks up ~1/1000 points that need manual correction.
Explainable Anomaly Detection in Images and Videos: A Survey
Anomaly detection and localization of visual data, including images and videos, are of great significance in both machine learning academia and applied real-world scenarios. Despite the rapid development of visual anomaly detection techniques in recent years, the interpretations of these black-box models and reasonable explanations of why anomalies can be distinguished out are scarce. This paper provides the first survey concentrated on explainable visual anomaly detection methods. We first introduce the basic background of image-level and video-level anomaly detection. Then, as the main content of this survey, a comprehensive and exhaustive literature review of explainable anomaly detection methods for both images and videos is presented. Next, we analyze why some explainable anomaly detection methods can be applied to both images and videos and why others can be only applied to one modality. Additionally, we provide summaries of current 2D visual anomaly detection datasets and evaluation metrics. Finally, we discuss several promising future directions and open problems to explore the explainability of 2D visual anomaly detection. The related resource collection is given at https://github.com/wyzjack/Awesome-XAD.
On Pairwise Clustering with Side Information
Pairwise clustering, in general, partitions a set of items via a known similarity function. In our treatment, clustering is modeled as a transductive prediction problem. Thus rather than beginning with a known similarity function, the function instead is hidden and the learner only receives a random sample consisting of a subset of the pairwise similarities. An additional set of pairwise side-information may be given to the learner, which then determines the inductive bias of our algorithms. We measure performance not based on the recovery of the hidden similarity function, but instead on how well we classify each item. We give tight bounds on the number of misclassifications. We provide two algorithms. The first algorithm SACA is a simple agglomerative clustering algorithm which runs in near linear time, and which serves as a baseline for our analyses. Whereas the second algorithm, RGCA, enables the incorporation of side-information which may lead to improved bounds at the cost of a longer running time.
DictAS: A Framework for Class-Generalizable Few-Shot Anomaly Segmentation via Dictionary Lookup
Recent vision-language models (e.g., CLIP) have demonstrated remarkable class-generalizable ability to unseen classes in few-shot anomaly segmentation (FSAS), leveraging supervised prompt learning or fine-tuning on seen classes. However, their cross-category generalization largely depends on prior knowledge of real seen anomaly samples. In this paper, we propose a novel framework, namely DictAS, which enables a unified model to detect visual anomalies in unseen object categories without any retraining on the target data, only employing a few normal reference images as visual prompts. The insight behind DictAS is to transfer dictionary lookup capabilities to the FSAS task for unseen classes via self-supervised learning, instead of merely memorizing the normal and abnormal feature patterns from the training set. Specifically, DictAS mainly consists of three components: (1) **Dictionary Construction** - to simulate the index and content of a real dictionary using features from normal reference images. (2) **Dictionary Lookup** - to retrieve queried region features from the dictionary via a sparse lookup strategy. When a query feature cannot be retrieved, it is classified as an anomaly. (3) **Query Discrimination Regularization**- to enhance anomaly discrimination by making abnormal features harder to retrieve from the dictionary. To achieve this, Contrastive Query Constraint and Text Alignment Constraint are further proposed. Extensive experiments on seven public industrial and medical datasets demonstrate that DictAS consistently outperforms state-of-the-art FSAS methods.
AnyLoss: Transforming Classification Metrics into Loss Functions
Many evaluation metrics can be used to assess the performance of models in binary classification tasks. However, most of them are derived from a confusion matrix in a non-differentiable form, making it very difficult to generate a differentiable loss function that could directly optimize them. The lack of solutions to bridge this challenge not only hinders our ability to solve difficult tasks, such as imbalanced learning, but also requires the deployment of computationally expensive hyperparameter search processes in model selection. In this paper, we propose a general-purpose approach that transforms any confusion matrix-based metric into a loss function, AnyLoss, that is available in optimization processes. To this end, we use an approximation function to make a confusion matrix represented in a differentiable form, and this approach enables any confusion matrix-based metric to be directly used as a loss function. The mechanism of the approximation function is provided to ensure its operability and the differentiability of our loss functions is proved by suggesting their derivatives. We conduct extensive experiments under diverse neural networks with many datasets, and we demonstrate their general availability to target any confusion matrix-based metrics. Our method, especially, shows outstanding achievements in dealing with imbalanced datasets, and its competitive learning speed, compared to multiple baseline models, underscores its efficiency.
Deep Graph-Level Orthogonal Hypersphere Compression for Anomaly Detection
Graph-level anomaly detection aims to identify anomalous graphs from a collection of graphs in an unsupervised manner. A common assumption of anomaly detection is that a reasonable decision boundary has a hypersphere shape, but may appear some non-conforming phenomena in high dimensions. Towards this end, we firstly propose a novel deep graph-level anomaly detection model, which learns the graph representation with maximum mutual information between substructure and global structure features while exploring a hypersphere anomaly decision boundary. The idea is to ensure the training data distribution consistent with the decision hypersphere via an orthogonal projection layer. Moreover, we further perform the bi-hypersphere compression to emphasize the discrimination of anomalous graphs from normal graphs. Note that our method is not confined to graph data and is applicable to anomaly detection of other data such as images. The numerical and visualization results on benchmark datasets demonstrate the effectiveness and superiority of our methods in comparison to many baselines and state-of-the-arts.
Predictive Multiplicity in Probabilistic Classification
Machine learning models are often used to inform real world risk assessment tasks: predicting consumer default risk, predicting whether a person suffers from a serious illness, or predicting a person's risk to appear in court. Given multiple models that perform almost equally well for a prediction task, to what extent do predictions vary across these models? If predictions are relatively consistent for similar models, then the standard approach of choosing the model that optimizes a penalized loss suffices. But what if predictions vary significantly for similar models? In machine learning, this is referred to as predictive multiplicity i.e. the prevalence of conflicting predictions assigned by near-optimal competing models. In this paper, we present a framework for measuring predictive multiplicity in probabilistic classification (predicting the probability of a positive outcome). We introduce measures that capture the variation in risk estimates over the set of competing models, and develop optimization-based methods to compute these measures efficiently and reliably for convex empirical risk minimization problems. We demonstrate the incidence and prevalence of predictive multiplicity in real-world tasks. Further, we provide insight into how predictive multiplicity arises by analyzing the relationship between predictive multiplicity and data set characteristics (outliers, separability, and majority-minority structure). Our results emphasize the need to report predictive multiplicity more widely.
Deep Learning on a Data Diet: Finding Important Examples Early in Training
Recent success in deep learning has partially been driven by training increasingly overparametrized networks on ever larger datasets. It is therefore natural to ask: how much of the data is superfluous, which examples are important for generalization, and how do we find them? In this work, we make the striking observation that, in standard vision datasets, simple scores averaged over several weight initializations can be used to identify important examples very early in training. We propose two such scores -- the Gradient Normed (GraNd) and the Error L2-Norm (EL2N) scores -- and demonstrate their efficacy on a range of architectures and datasets by pruning significant fractions of training data without sacrificing test accuracy. In fact, using EL2N scores calculated a few epochs into training, we can prune half of the CIFAR10 training set while slightly improving test accuracy. Furthermore, for a given dataset, EL2N scores from one architecture or hyperparameter configuration generalize to other configurations. Compared to recent work that prunes data by discarding examples that are rarely forgotten over the course of training, our scores use only local information early in training. We also use our scores to detect noisy examples and study training dynamics through the lens of important examples -- we investigate how the data distribution shapes the loss surface and identify subspaces of the model's data representation that are relatively stable over training.
Fidelity Isn't Accuracy: When Linearly Decodable Functions Fail to Match the Ground Truth
Neural networks excel as function approximators, but their complexity often obscures the types of functions they learn, making it difficult to explain their behavior. To address this, the linearity score lambda(f) is introduced, a simple and interpretable diagnostic that quantifies how well a regression network's output can be mimicked by a linear model. Defined as the R^2 value between the network's predictions and those of a trained linear surrogate, lambda(f) measures linear decodability: the extent to which the network's behavior aligns with a structurally simple model. This framework is evaluated on both synthetic and real-world datasets, using dataset-specific networks and surrogates. High lambda(f) scores reliably indicate alignment with the network's outputs; however, they do not guarantee accuracy with respect to the ground truth. These results highlight the risk of using surrogate fidelity as a proxy for model understanding, especially in high-stakes regression tasks.
Detecting Spelling and Grammatical Anomalies in Russian Poetry Texts
The quality of natural language texts in fine-tuning datasets plays a critical role in the performance of generative models, particularly in computational creativity tasks such as poem or song lyric generation. Fluency defects in generated poems significantly reduce their value. However, training texts are often sourced from internet-based platforms without stringent quality control, posing a challenge for data engineers to manage defect levels effectively. To address this issue, we propose the use of automated linguistic anomaly detection to identify and filter out low-quality texts from training datasets for creative models. In this paper, we present a comprehensive comparison of unsupervised and supervised text anomaly detection approaches, utilizing both synthetic and human-labeled datasets. We also introduce the RUPOR dataset, a collection of Russian-language human-labeled poems designed for cross-sentence grammatical error detection, and provide the full evaluation code. Our work aims to empower the community with tools and insights to improve the quality of training datasets for generative models in creative domains.
Detection of Conspiracy Theories Beyond Keyword Bias in German-Language Telegram Using Large Language Models
The automated detection of conspiracy theories online typically relies on supervised learning. However, creating respective training data requires expertise, time and mental resilience, given the often harmful content. Moreover, available datasets are predominantly in English and often keyword-based, introducing a token-level bias into the models. Our work addresses the task of detecting conspiracy theories in German Telegram messages. We compare the performance of supervised fine-tuning approaches using BERT-like models with prompt-based approaches using Llama2, GPT-3.5, and GPT-4 which require little or no additional training data. We use a dataset of sim!! 4,000 messages collected during the COVID-19 pandemic, without the use of keyword filters. Our findings demonstrate that both approaches can be leveraged effectively: For supervised fine-tuning, we report an F1 score of sim!! 0.8 for the positive class, making our model comparable to recent models trained on keyword-focused English corpora. We demonstrate our model's adaptability to intra-domain temporal shifts, achieving F1 scores of sim!! 0.7. Among prompting variants, the best model is GPT-4, achieving an F1 score of sim!! 0.8 for the positive class in a zero-shot setting and equipped with a custom conspiracy theory definition.
CLIP-AD: A Language-Guided Staged Dual-Path Model for Zero-shot Anomaly Detection
This paper considers zero-shot Anomaly Detection (AD), performing AD without reference images of the test objects. We propose a framework called CLIP-AD to leverage the zero-shot capabilities of the large vision-language model CLIP. Firstly, we reinterpret the text prompts design from a distributional perspective and propose a Representative Vector Selection (RVS) paradigm to obtain improved text features. Secondly, we note opposite predictions and irrelevant highlights in the direct computation of the anomaly maps. To address these issues, we introduce a Staged Dual-Path model (SDP) that leverages features from various levels and applies architecture and feature surgery. Lastly, delving deeply into the two phenomena, we point out that the image and text features are not aligned in the joint embedding space. Thus, we introduce a fine-tuning strategy by adding linear layers and construct an extended model SDP+, further enhancing the performance. Abundant experiments demonstrate the effectiveness of our approach, e.g., on MVTec-AD, SDP outperforms the SOTA WinCLIP by +4.2/+10.7 in segmentation metrics F1-max/PRO, while SDP+ achieves +8.3/+20.5 improvements.
Detecting Errors in a Numerical Response via any Regression Model
Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.
SMUG-Explain: A Framework for Symbolic Music Graph Explanations
In this work, we present Score MUsic Graph (SMUG)-Explain, a framework for generating and visualizing explanations of graph neural networks applied to arbitrary prediction tasks on musical scores. Our system allows the user to visualize the contribution of input notes (and note features) to the network output, directly in the context of the musical score. We provide an interactive interface based on the music notation engraving library Verovio. We showcase the usage of SMUG-Explain on the task of cadence detection in classical music. All code is available on https://github.com/manoskary/SMUG-Explain.
Leveraging Multimodal LLM Descriptions of Activity for Explainable Semi-Supervised Video Anomaly Detection
Existing semi-supervised video anomaly detection (VAD) methods often struggle with detecting complex anomalies involving object interactions and generally lack explainability. To overcome these limitations, we propose a novel VAD framework leveraging Multimodal Large Language Models (MLLMs). Unlike previous MLLM-based approaches that make direct anomaly judgments at the frame level, our method focuses on extracting and interpreting object activity and interactions over time. By querying an MLLM with visual inputs of object pairs at different moments, we generate textual descriptions of the activity and interactions from nominal videos. These textual descriptions serve as a high-level representation of the activity and interactions of objects in a video. They are used to detect anomalies during test time by comparing them to textual descriptions found in nominal training videos. Our approach inherently provides explainability and can be combined with many traditional VAD methods to further enhance their interpretability. Extensive experiments on benchmark datasets demonstrate that our method not only detects complex interaction-based anomalies effectively but also achieves state-of-the-art performance on datasets without interaction anomalies.
Exploring the cloud of feature interaction scores in a Rashomon set
Interactions among features are central to understanding the behavior of machine learning models. Recent research has made significant strides in detecting and quantifying feature interactions in single predictive models. However, we argue that the feature interactions extracted from a single pre-specified model may not be trustworthy since: a well-trained predictive model may not preserve the true feature interactions and there exist multiple well-performing predictive models that differ in feature interaction strengths. Thus, we recommend exploring feature interaction strengths in a model class of approximately equally accurate predictive models. In this work, we introduce the feature interaction score (FIS) in the context of a Rashomon set, representing a collection of models that achieve similar accuracy on a given task. We propose a general and practical algorithm to calculate the FIS in the model class. We demonstrate the properties of the FIS via synthetic data and draw connections to other areas of statistics. Additionally, we introduce a Halo plot for visualizing the feature interaction variance in high-dimensional space and a swarm plot for analyzing FIS in a Rashomon set. Experiments with recidivism prediction and image classification illustrate how feature interactions can vary dramatically in importance for similarly accurate predictive models. Our results suggest that the proposed FIS can provide valuable insights into the nature of feature interactions in machine learning models.
Robustness and Accuracy Could Be Reconcilable by (Proper) Definition
The trade-off between robustness and accuracy has been widely studied in the adversarial literature. Although still controversial, the prevailing view is that this trade-off is inherent, either empirically or theoretically. Thus, we dig for the origin of this trade-off in adversarial training and find that it may stem from the improperly defined robust error, which imposes an inductive bias of local invariance -- an overcorrection towards smoothness. Given this, we advocate employing local equivariance to describe the ideal behavior of a robust model, leading to a self-consistent robust error named SCORE. By definition, SCORE facilitates the reconciliation between robustness and accuracy, while still handling the worst-case uncertainty via robust optimization. By simply substituting KL divergence with variants of distance metrics, SCORE can be efficiently minimized. Empirically, our models achieve top-rank performance on RobustBench under AutoAttack. Besides, SCORE provides instructive insights for explaining the overfitting phenomenon and semantic input gradients observed on robust models. Code is available at https://github.com/P2333/SCORE.
VarAD: Lightweight High-Resolution Image Anomaly Detection via Visual Autoregressive Modeling
This paper addresses a practical task: High-Resolution Image Anomaly Detection (HRIAD). In comparison to conventional image anomaly detection for low-resolution images, HRIAD imposes a heavier computational burden and necessitates superior global information capture capacity. To tackle HRIAD, this paper translates image anomaly detection into visual token prediction and proposes VarAD based on visual autoregressive modeling for token prediction. Specifically, VarAD first extracts multi-hierarchy and multi-directional visual token sequences, and then employs an advanced model, Mamba, for visual autoregressive modeling and token prediction. During the prediction process, VarAD effectively exploits information from all preceding tokens to predict the target token. Finally, the discrepancies between predicted tokens and original tokens are utilized to score anomalies. Comprehensive experiments on four publicly available datasets and a real-world button inspection dataset demonstrate that the proposed VarAD achieves superior high-resolution image anomaly detection performance while maintaining lightweight, rendering VarAD a viable solution for HRIAD. Code is available at https://github.com/caoyunkang/VarAD{https://github.com/caoyunkang/VarAD}.
Crane: Context-Guided Prompt Learning and Attention Refinement for Zero-Shot Anomaly Detection
Anomaly Detection involves identifying deviations from normal data distributions and is critical in fields such as medical diagnostics and industrial defect detection. Traditional AD methods typically require the availability of normal training samples; however, this assumption is not always feasible. Recently, the rich pretraining knowledge of CLIP has shown promising zero-shot generalization in detecting anomalies without the need for training samples from target domains. However, CLIP's coarse-grained image-text alignment limits localization and detection performance for fine-grained anomalies due to: (1) spatial misalignment, and (2) the limited sensitivity of global features to local anomalous patterns. In this paper, we propose Crane which tackles both problems. First, we introduce a correlation-based attention module to retain spatial alignment more accurately. Second, to boost the model's awareness of fine-grained anomalies, we condition the learnable prompts of the text encoder on image context extracted from the vision encoder and perform a local-to-global representation fusion. Moreover, our method can incorporate vision foundation models such as DINOv2 to further enhance spatial understanding and localization. The key insight of Crane is to balance learnable adaptations for modeling anomalous concepts with non-learnable adaptations that preserve and exploit generalized pretrained knowledge, thereby minimizing in-domain overfitting and maximizing performance on unseen domains. Extensive evaluation across 14 diverse industrial and medical datasets demonstrates that Crane consistently improves the state-of-the-art ZSAD from 2% to 28%, at both image and pixel levels, while remaining competitive in inference speed. The code is available at https://github.com/AlirezaSalehy/Crane.
Towards Zero-shot 3D Anomaly Localization
3D anomaly detection and localization is of great significance for industrial inspection. Prior 3D anomaly detection and localization methods focus on the setting that the testing data share the same category as the training data which is normal. However, in real-world applications, the normal training data for the target 3D objects can be unavailable due to issues like data privacy or export control regulation. To tackle these challenges, we identify a new task -- zero-shot 3D anomaly detection and localization, where the training and testing classes do not overlap. To this end, we design 3DzAL, a novel patch-level contrastive learning framework based on pseudo anomalies generated using the inductive bias from task-irrelevant 3D xyz data to learn more representative feature representations. Furthermore, we train a normalcy classifier network to classify the normal patches and pseudo anomalies and utilize the classification result jointly with feature distance to design anomaly scores. Instead of directly using the patch point clouds, we introduce adversarial perturbations to the input patch xyz data before feeding into the 3D normalcy classifier for the classification-based anomaly score. We show that 3DzAL outperforms the state-of-the-art anomaly detection and localization performance.
Conformal Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularization
We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.
Learn to Rank Risky Investors: A Case Study of Predicting Retail Traders' Behaviour and Profitability
Identifying risky traders with high profits in financial markets is crucial for market makers, such as trading exchanges, to ensure effective risk management through real-time decisions on regulation compliance and hedging. However, capturing the complex and dynamic behaviours of individual traders poses significant challenges. Traditional classification and anomaly detection methods often establish a fixed risk boundary, failing to account for this complexity and dynamism. To tackle this issue, we propose a profit-aware risk ranker (PA-RiskRanker) that reframes the problem of identifying risky traders as a ranking task using Learning-to-Rank (LETOR) algorithms. Our approach features a Profit-Aware binary cross entropy (PA-BCE) loss function and a transformer-based ranker enhanced with a self-cross-trader attention pipeline. These components effectively integrate profit and loss (P&L) considerations into the training process while capturing intra- and inter-trader relationships. Our research critically examines the limitations of existing deep learning-based LETOR algorithms in trading risk management, which often overlook the importance of P&L in financial scenarios. By prioritising P&L, our method improves risky trader identification, achieving an 8.4% increase in F1 score compared to state-of-the-art (SOTA) ranking models like Rankformer. Additionally, it demonstrates a 10%-17% increase in average profit compared to all benchmark models.
Preserving Statistical Validity in Adaptive Data Analysis
A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples. We show that, surprisingly, there is a way to estimate an exponential in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.
AnomalyCLIP: Object-agnostic Prompt Learning for Zero-shot Anomaly Detection
Zero-shot anomaly detection (ZSAD) requires detection models trained using auxiliary data to detect anomalies without any training sample in a target dataset. It is a crucial task when training data is not accessible due to various concerns, eg, data privacy, yet it is challenging since the models need to generalize to anomalies across different domains where the appearance of foreground objects, abnormal regions, and background features, such as defects/tumors on different products/organs, can vary significantly. Recently large pre-trained vision-language models (VLMs), such as CLIP, have demonstrated strong zero-shot recognition ability in various vision tasks, including anomaly detection. However, their ZSAD performance is weak since the VLMs focus more on modeling the class semantics of the foreground objects rather than the abnormality/normality in the images. In this paper we introduce a novel approach, namely AnomalyCLIP, to adapt CLIP for accurate ZSAD across different domains. The key insight of AnomalyCLIP is to learn object-agnostic text prompts that capture generic normality and abnormality in an image regardless of its foreground objects. This allows our model to focus on the abnormal image regions rather than the object semantics, enabling generalized normality and abnormality recognition on diverse types of objects. Large-scale experiments on 17 real-world anomaly detection datasets show that AnomalyCLIP achieves superior zero-shot performance of detecting and segmenting anomalies in datasets of highly diverse class semantics from various defect inspection and medical imaging domains. Code will be made available at https://github.com/zqhang/AnomalyCLIP.
Deep Anomaly Detection with Outlier Exposure
It is important to detect anomalous inputs when deploying machine learning systems. The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples. At the same time, diverse image and text data are available in enormous quantities. We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE). This enables anomaly detectors to generalize and detect unseen anomalies. In extensive experiments on natural language processing and small- and large-scale vision tasks, we find that Outlier Exposure significantly improves detection performance. We also observe that cutting-edge generative models trained on CIFAR-10 may assign higher likelihoods to SVHN images than to CIFAR-10 images; we use OE to mitigate this issue. We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.
Generalization is not a universal guarantee: Estimating similarity to training data with an ensemble out-of-distribution metric
Failure of machine learning models to generalize to new data is a core problem limiting the reliability of AI systems, partly due to the lack of simple and robust methods for comparing new data to the original training dataset. We propose a standardized approach for assessing data similarity in a model-agnostic manner by constructing a supervised autoencoder for generalizability estimation (SAGE). We compare points in a low-dimensional embedded latent space, defining empirical probability measures for k-Nearest Neighbors (kNN) distance, reconstruction of inputs and task-based performance. As proof of concept for classification tasks, we use MNIST and CIFAR-10 to demonstrate how an ensemble output probability score can separate deformed images from a mixture of typical test examples, and how this SAGE score is robust to transformations of increasing severity. As further proof of concept, we extend this approach to a regression task using non-imaging data (UCI Abalone). In all cases, we show that out-of-the-box model performance increases after SAGE score filtering, even when applied to data from the model's own training and test datasets. Our out-of-distribution scoring method can be introduced during several steps of model construction and assessment, leading to future improvements in responsible deep learning implementation.
Anomaly Detection using Autoencoders in High Performance Computing Systems
Anomaly detection in supercomputers is a very difficult problem due to the big scale of the systems and the high number of components. The current state of the art for automated anomaly detection employs Machine Learning methods or statistical regression models in a supervised fashion, meaning that the detection tool is trained to distinguish among a fixed set of behaviour classes (healthy and unhealthy states). We propose a novel approach for anomaly detection in High Performance Computing systems based on a Machine (Deep) Learning technique, namely a type of neural network called autoencoder. The key idea is to train a set of autoencoders to learn the normal (healthy) behaviour of the supercomputer nodes and, after training, use them to identify abnormal conditions. This is different from previous approaches which where based on learning the abnormal condition, for which there are much smaller datasets (since it is very hard to identify them to begin with). We test our approach on a real supercomputer equipped with a fine-grained, scalable monitoring infrastructure that can provide large amount of data to characterize the system behaviour. The results are extremely promising: after the training phase to learn the normal system behaviour, our method is capable of detecting anomalies that have never been seen before with a very good accuracy (values ranging between 88% and 96%).
Supersparse Linear Integer Models for Optimized Medical Scoring Systems
Scoring systems are linear classification models that only require users to add, subtract and multiply a few small numbers in order to make a prediction. These models are in widespread use by the medical community, but are difficult to learn from data because they need to be accurate and sparse, have coprime integer coefficients, and satisfy multiple operational constraints. We present a new method for creating data-driven scoring systems called a Supersparse Linear Integer Model (SLIM). SLIM scoring systems are built by solving an integer program that directly encodes measures of accuracy (the 0-1 loss) and sparsity (the ell_0-seminorm) while restricting coefficients to coprime integers. SLIM can seamlessly incorporate a wide range of operational constraints related to accuracy and sparsity, and can produce highly tailored models without parameter tuning. We provide bounds on the testing and training accuracy of SLIM scoring systems, and present a new data reduction technique that can improve scalability by eliminating a portion of the training data beforehand. Our paper includes results from a collaboration with the Massachusetts General Hospital Sleep Laboratory, where SLIM was used to create a highly tailored scoring system for sleep apnea screening
