# ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions

arXiv: https://arxiv.org/abs/2201.00382 · HTML: https://mlsanity.com/paper/2201.00382/

## Key facts

- Cited by 153 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 80 references that are in the map.
- First posted on arXiv 2 Jan 2022.

## Builds on (most cited first, 18 of 18)

- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [OPV2V: An Open Benchmark Dataset and Fusion Pipeline for Perception with Vehicle-to-Vehicle Communication](https://mlsanity.com/paper/2109.07644/) (2021)
- [Therapeutics Data Commons: Machine Learning Datasets and Tasks for Drug Discovery and Development](https://mlsanity.com/paper/2102.09548/) (2021)
- [Enhancing Graph Neural Network-based Fraud Detectors against Camouflaged Fraudsters](https://mlsanity.com/paper/2008.08692/) (2020)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [Optimal Sparse Decision Trees](https://mlsanity.com/paper/1904.12847/) (2019)
- [Generative Adversarial Active Learning for Unsupervised Outlier Detection](https://mlsanity.com/paper/1809.10816/) (2018)
- [Automated Self-Supervised Learning for Graphs](https://mlsanity.com/paper/2106.05470/) (2021)
- [MIMOSA: Multi-constraint Molecule Sampling for Molecule Optimization](https://mlsanity.com/paper/2010.02318/) (2020)
- [HINT: Hierarchical Interaction Network for Trial Outcome Prediction Leveraging Web Data](https://mlsanity.com/paper/2102.04252/) (2021)
- [XGBOD: Improving Supervised Outlier Detection with Unsupervised Representation Learning](https://mlsanity.com/paper/1912.00290/) (2019)
- [Toward Deep Supervised Anomaly Detection: Reinforcement Learning from Partially Labeled Anomaly Data](https://mlsanity.com/paper/2009.06847/) (2020)
- [TODS: An Automated Time Series Outlier Detection System](https://mlsanity.com/paper/2009.09822/) (2020)
- [Meta-AAD: Active Anomaly Detection with Deep Reinforcement Learning](https://mlsanity.com/paper/2009.07415/) (2020)
- [LSCP: Locally Selective Combination in Parallel Outlier Ensembles](https://mlsanity.com/paper/1812.01528/) (2018)
- [SYNC: A Copula based Framework for Generating Synthetic Data from Aggregated Sources](https://mlsanity.com/paper/2009.09471/) (2020)
- [A Large-scale Study on Unsupervised Outlier Model Selection: Do Internal Strategies Suffice?](https://mlsanity.com/paper/2104.01422/) (2021)
- [Holistic Grid Fusion Based Stop Line Estimation](https://mlsanity.com/paper/2009.09093/) (2020)

## Built on by (most cited first, 30 of 153)

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- [BOND: Benchmarking Unsupervised Outlier Node Detection on Static Attributed Graphs](https://mlsanity.com/paper/2206.10071/) (2022)
- [On Diffusion Modeling for Anomaly Detection](https://mlsanity.com/paper/2305.18593/) (2023)
- [Calibrated One-class Classification for Unsupervised Time Series Anomaly Detection](https://mlsanity.com/paper/2207.12201/) (2022)
- [PyGOD: A Python Library for Graph Outlier Detection](https://mlsanity.com/paper/2204.12095/) (2022)
- [AD-LLM: Benchmarking Large Language Models for Anomaly Detection](https://mlsanity.com/paper/2412.11142/) (2024)
- [Unsupervised anomaly detection algorithms on real-world data: how many do we need?](https://mlsanity.com/paper/2305.00735/) (2023)
- [NLP-ADBench: NLP Anomaly Detection Benchmark](https://mlsanity.com/paper/2412.04784/) (2024)
- [NNG-Mix: Improving Semi-supervised Anomaly Detection with Pseudo-anomaly Generation](https://mlsanity.com/paper/2311.11961/) (2023)
- [Anomaly Detection of Tabular Data Using LLMs](https://mlsanity.com/paper/2406.16308/) (2024)
- [AnoShift: A Distribution Shift Benchmark for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2206.15476/) (2022)
- [ADGym: Design Choices for Deep Anomaly Detection](https://mlsanity.com/paper/2309.15376/) (2023)
- [Unsupervised Anomaly Detection with Rejection](https://mlsanity.com/paper/2305.13189/) (2023)
- [ClimateLLM: Efficient Weather Forecasting via Frequency-Aware Large Language Models](https://mlsanity.com/paper/2502.11059/) (2025)
- [Intrinsic Self-Supervision for Data Quality Audits](https://mlsanity.com/paper/2305.17048/) (2023)
- [Anomaly Detection with Variance Stabilized Density Estimation](https://mlsanity.com/paper/2306.00582/) (2023)
- [UADB: Unsupervised Anomaly Detection Booster](https://mlsanity.com/paper/2306.01997/) (2023)
- [Anomaly Detection and Generation with Diffusion Models: A Survey](https://mlsanity.com/paper/2506.09368/) (2025)
- [ODIM: Outlier Detection via Likelihood of Under-Fitted Generative Models](https://mlsanity.com/paper/2301.04257/) (2023)
- [Anomaly Detection with Score Distribution Discrimination](https://mlsanity.com/paper/2306.14403/) (2023)
- [Unsupervised Skin Lesion Segmentation via Structural Entropy Minimization on Multi-Scale Superpixel Graphs](https://mlsanity.com/paper/2309.01899/) (2023)
- [The OPS-SAT benchmark for detecting anomalies in satellite telemetry](https://mlsanity.com/paper/2407.04730/) (2024)
- [TACTIC for Navigating the Unknown: Tabular Anomaly deteCTion via In-Context inference](https://mlsanity.com/paper/2603.14171/) (2026)
- [Towards Fair Graph Anomaly Detection: Problem, Benchmark Datasets, and Evaluation](https://mlsanity.com/paper/2402.15988/) (2024)
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## Abstract (arXiv)

Outlier detection refers to the identification of data points that deviate from a general data distribution. Existing unsupervised approaches often suffer from high computational cost, complex hyperparameter tuning, and limited interpretability, especially when working with large, high-dimensional datasets. To address these issues, we present a simple yet effective algorithm called ECOD (Empirical-Cumulative-distribution-based Outlier Detection), which is inspired by the fact that outliers are often the "rare events" that appear in the tails of a distribution. In a nutshell, ECOD first estimates the underlying distribution of the input data in a nonparametric fashion by computing the empirical cumulative distribution per dimension of the data. ECOD then uses these empirical distributions to estimate tail probabilities per dimension for each data point. Finally, ECOD computes an outlier score of each data point by aggregating estimated tail probabilities across dimensions. Our contributions are as follows: (1) we propose a novel outlier detection method called ECOD, which is both parameter-free and easy to interpret; (2) we perform extensive experiments on 30 benchmark datasets, where we find that ECOD outperforms 11 state-of-the-art baselines in terms of accuracy, efficiency, and scalability; and (3) we release an easy-to-use and scalable (with distributed support) Python implementation for accessibility and reproducibility.