High-dimensional and Permutation Invariant Anomaly Detection

TL;DR

This paper introduces a permutation-invariant diffusion-based density estimator tailored for high-dimensional particle physics data, enabling effective anomaly detection of jets with variable-length inputs and demonstrating its advantages over supervised methods.

Contribution

The work presents a novel permutation-invariant density estimation technique using diffusion models for high-dimensional, variable-length particle physics data, improving anomaly detection capabilities.

Findings

Effective identification of anomalous jets using the learned density score.

Comparison shows the density ratio aligns well with supervised classification results.

Demonstrates the method's ability to handle complex, high-dimensional data.

Abstract

Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable properties such as permutation invariance and variable-length inputs becomes difficult within popular density estimation methods. In this work, we introduce a permutation-invariant density estimator for particle physics data based on diffusion models, specifically designed to handle variable-length inputs. We demonstrate the efficacy of our methodology by utilizing the learned density as a permutation-invariant anomaly detection score, effectively identifying jets with low likelihood under the background-only hypothesis. To validate our density estimation method, we investigate the ratio of learned densities and compare to those obtained by a supervised classification algorithm.