# COPOD: Copula-Based Outlier Detection

arXiv: https://arxiv.org/abs/2009.09463 · HTML: https://mlsanity.com/paper/2009.09463/

## Key facts

- Cited by 146 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Sep 2020.

## Built on by (most cited first, 30 of 146)

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- [ODIM: Outlier Detection via Likelihood of Under-Fitted Generative Models](https://mlsanity.com/paper/2301.04257/) (2023)
- [The OPS-SAT benchmark for detecting anomalies in satellite telemetry](https://mlsanity.com/paper/2407.04730/) (2024)
- [mTSBench: Benchmarking Multivariate Time Series Anomaly Detection and Model Selection at Scale](https://mlsanity.com/paper/2506.21550/) (2025)
- [PaAno: Patch-Based Representation Learning for Time-Series Anomaly Detection](https://mlsanity.com/paper/2602.01359/) (2026)
- [TACTIC for Navigating the Unknown: Tabular Anomaly deteCTion via In-Context inference](https://mlsanity.com/paper/2603.14171/) (2026)
- [TOD: GPU-accelerated Outlier Detection via Tensor Operations](https://mlsanity.com/paper/2110.14007/) (2021)
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- [Retrieval Augmented Deep Anomaly Detection for Tabular Data](https://mlsanity.com/paper/2401.17052/) (2024)
- [TAD-Bench: A Comprehensive Benchmark for Embedding-Based Text Anomaly Detection](https://mlsanity.com/paper/2501.11960/) (2025)

## 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.