# Null Hypothesis Test for Anomaly Detection

arXiv: https://arxiv.org/abs/2210.02226 · HTML: https://mlsanity.com/paper/2210.02226/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 5 Oct 2022.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [Learning new physics efficiently with nonparametric methods](https://mlsanity.com/paper/2204.02317/) (2022)

## Built on by (most cited first, 7 of 7)

- [Anomalies, Representations, and Self-Supervision](https://mlsanity.com/paper/2301.04660/) (2023)
- [Improving new physics searches with diffusion models for event observables and jet constituents](https://mlsanity.com/paper/2312.10130/) (2023)
- [Model-Agnostic Signal Discovery with Machine Learning: Bridging the Gap Between Theory and Practice](https://mlsanity.com/paper/2605.31103/) (2026)
- [Decorrelation with conditional normalizing flows](https://mlsanity.com/paper/2211.02486/) (2022)
- [TRANSIT your events into a new mass: Fast background interpolation for weakly-supervised anomaly searches](https://mlsanity.com/paper/2503.04342/) (2025)
- [Mutual Information Surprise: Rethinking Unexpectedness in Autonomous Systems](https://mlsanity.com/paper/2508.17403/) (2025)
- [Refining Decision Boundaries In Anomaly Detection Using Similarity Search Within the Feature Space](https://mlsanity.com/paper/2602.02925/) (2026)

## Abstract (arXiv)

We extend the use of Classification Without Labels for anomaly detection with a hypothesis test designed to exclude the background-only hypothesis. By testing for statistical independence of the two discriminating dataset regions, we are able to exclude the background-only hypothesis without relying on fixed anomaly score cuts or extrapolations of background estimates between regions. The method relies on the assumption of conditional independence of anomaly score features and dataset regions, which can be ensured using existing decorrelation techniques. As a benchmark example, we consider the LHC Olympics dataset where we show that mutual information represents a suitable test for statistical independence and our method exhibits excellent and robust performance at different signal fractions even in presence of realistic feature correlations.