mlsanityData to 7 Oct 2026

COPOD: Copula-Based Outlier Detection

arXiv 2009.09463 ↗First posted 20 Sep 2020stat.ML cs.IR cs.LGcited by 143

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Abstract (arXiv)

Outlier detection refers to the identification of rare items that are deviant from the general data distribution. Existing approaches suffer from high computational complexity, low predictive capability, and limited interpretability. As a remedy, we present a novel outlier detection algorithm called COPOD, which is inspired by copulas for modeling multivariate data distribution. COPOD first constructs an empirical copula, and then uses it to predict tail probabilities of each given data point to determine its level of "extremeness". Intuitively, we think of this as calculating an anomalous p-value. This makes COPOD both parameter-free, highly interpretable, and computationally efficient. In this work, we make three key contributions, 1) propose a novel, parameter-free outlier detection algorithm with both great performance and interpretability, 2) perform extensive experiments on 30 benchmark datasets to show that COPOD outperforms in most cases and is also one of the fastest algorithms, and 3) release an easy-to-use Python implementation for reproducibility.

Key facts. Cited by 143 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Sep 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 12; 2022: 20; 2023: 25; 2024: 19; 2025: 27; 2026: 40.

143 papers.

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  1. 2022ADBench: Anomaly Detection Benchmarkcited by 230
  2. 2022Deep Isolation Forest for Anomaly Detectioncited by 90
  3. 2023On Diffusion Modeling for Anomaly Detectioncited by 71
  4. 2023Unsupervised anomaly detection algorithms on real-world data: how many do we need?cited by 20
  5. 2021Deep Clustering based Fair Outlier Detectioncited by 19
  6. 2021Backdoor Attack through Frequency Domaincited by 18
  7. 2022Data-Efficient and Interpretable Tabular Anomaly Detectioncited by 15
  8. 2022Estimating the Contamination Factor's Distribution in Unsupervised Anomaly Detectioncited by 14
  9. 2023Beyond Individual Input for Deep Anomaly Detection on Tabular Datacited by 14
  10. 2022Data-SUITE: Data-centric identification of in-distribution incongruous examplescited by 12
  11. 2022AnoShift: A Distribution Shift Benchmark for Unsupervised Anomaly Detectioncited by 11
  12. 2022Adversarial Camouflage for Node Injection Attack on Graphscited by 11
38 more
  1. 2023RoSAS: Deep Semi-Supervised Anomaly Detection with Contamination-Resilient Continuous Supervisioncited by 11
  2. 2023ADGym: Design Choices for Deep Anomaly Detectioncited by 11
  3. 2023Open-Set Likelihood Maximization for Few-Shot Learningcited by 10
  4. 2023Unsupervised Anomaly Detection with Rejectioncited by 9
  5. 2024A Large-Scale Simulation on Large Language Models for Decision-Making in Political Sciencecited by 9
  6. 2022Suppressing Poisoning Attacks on Federated Learning for Medical Imagingcited by 8
  7. 2023Lifelong Continual Learning for Anomaly Detection: New Challenges, Perspectives, and Insightscited by 8
  8. 2023Anomaly Detection with Variance Stabilized Density Estimationcited by 8
  9. 2023UADB: Unsupervised Anomaly Detection Boostercited by 7
  10. 2024The OPS-SAT benchmark for detecting anomalies in satellite telemetrycited by 7
  11. 2021TOD: GPU-accelerated Outlier Detection via Tensor Operationscited by 6
  12. 2022Explainable Artificial Intelligence and Causal Inference based ATM Fraud Detectioncited by 6
  13. 2023ODIM: Outlier Detection via Likelihood of Under-Fitted Generative Modelscited by 6
  14. 2024Retrieval Augmented Deep Anomaly Detection for Tabular Datacited by 6
  15. 2025TAD-Bench: A Comprehensive Benchmark for Embedding-Based Text Anomaly Detectioncited by 6
  16. 2025Subject Information Extraction for Novelty Detection with Domain Shiftscited by 6
  17. 2025mTSBench: Benchmarking Multivariate Time Series Anomaly Detection and Model Selection at Scalecited by 6
  18. 2022GraphAD: A Graph Neural Network for Entity-Wise Multivariate Time-Series Anomaly Detectioncited by 5
  19. 2022Inference and Sampling for Archimax Copulascited by 5
  20. 2022A Comprehensive Review of Trends, Applications and Challenges In Out-of-Distribution Detectioncited by 5
  21. 2022D.MCA: Outlier Detection with Explicit Micro-Cluster Assignmentscited by 5
  22. 2022AD-DMKDE: Anomaly Detection through Density Matrices and Fourier Featurescited by 5
  23. 2023TabADM: Unsupervised Tabular Anomaly Detection with Diffusion Modelscited by 5
  24. 2025Evaluation of (Un-)Supervised Machine Learning Methods for GNSS Interference Classification with Real-World Data Discrepanciescited by 5
  25. 2025xLSTMAD: A Powerful xLSTM-based Method for Anomaly Detectioncited by 5
  26. 2025Text Anomaly Detection with Simplified Isolation Kernelcited by 5
  27. 2026PaAno: Patch-Based Representation Learning for Time-Series Anomaly Detectioncited by 5
  28. 2021Locally Interpretable One-Class Anomaly Detection for Credit Card Fraud Detectioncited by 4
  29. 2022Time Series Anomaly Detection via Reinforcement Learning-Based Model Selectioncited by 4
  30. 2022Anomaly detection using data depth: multivariate casecited by 4
  31. 2023Comparative Evaluation of Anomaly Detection Methods for Fraud Detection in Online Credit Card Paymentscited by 4
  32. 2024Disentangling Tabular Data Towards Better One-Class Anomaly Detectioncited by 4
  33. 2025Unsupervised Anomaly Detection through Mass Repulsing Optimal Transportcited by 4
  34. 2025We Need to Rethink Benchmarking in Anomaly Detectioncited by 4
  35. 2026TACTIC for Navigating the Unknown: Tabular Anomaly deteCTion via In-Context inferencecited by 4
  36. 2026Between Resolution Collapse and Variance Inflation: Weighted Conformal Anomaly Detection in Low-Data Regimescited by 4
  37. 2023Adaptive Thresholding Heuristic for KPI Anomaly Detectioncited by 3
  38. 2024Anomaly Prediction: A Novel Approach with Explicit Delay and Horizoncited by 3

50 most cited of 143 All 143 (JSON)