COPOD: Copula-Based Outlier Detection

TLDR

Outlier detection identifies rare items deviating from the general data distribution, yet existing methods suffer from high computational complexity, low predictive capability, and limited interpretability. The study proposes COPOD, a novel parameter‑free outlier detection algorithm inspired by copulas, aiming to deliver high performance, interpretability, extensive benchmarking on 30 datasets, and an open‑source Python implementation. COPOD constructs an empirical copula and uses it to compute tail probabilities for each data point, effectively estimating an anomalous p‑value to assess extremeness. COPOD is parameter‑free, highly interpretable, computationally efficient, and outperforms most competing methods on 30 benchmark datasets while being among the fastest.

Abstract

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.