Null Hypothesis Test for Anomaly Detection

TL;DR

This paper introduces a hypothesis testing method for anomaly detection that assesses statistical independence between dataset regions, improving robustness and avoiding fixed thresholds, demonstrated on LHC Olympics data.

Contribution

It extends classification without labels by incorporating a hypothesis test for background-only hypothesis exclusion, leveraging mutual information and decorrelation techniques.

Findings

The method effectively detects anomalies across various signal fractions.

It maintains high performance even with realistic feature correlations.

Mutual information is a suitable test statistic for independence.

Abstract

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.