Perfect density models cannot guarantee anomaly detection

TL;DR

This paper critically examines the use of likelihood-based density models for anomaly detection, revealing that such likelihoods are unreliable indicators due to underlying assumptions and reparametrization issues.

Contribution

It demonstrates that density values from perfect models do not reliably indicate anomalies and emphasizes the need to explicitly state assumptions in anomaly detection methods.

Findings

Likelihoods can be misleading for anomaly detection

Reparametrization affects the interpretability of density values

Explicit assumptions are necessary for reliable anomaly detection

Abstract

Thanks to the tractability of their likelihood, several deep generative models show promise for seemingly straightforward but important applications like anomaly detection, uncertainty estimation, and active learning. However, the likelihood values empirically attributed to anomalies conflict with the expectations these proposed applications suggest. In this paper, we take a closer look at the behavior of distribution densities through the lens of reparametrization and show that these quantities carry less meaningful information than previously thought, beyond estimation issues or the curse of dimensionality. We conclude that the use of these likelihoods for anomaly detection relies on strong and implicit hypotheses, and highlight the necessity of explicitly formulating these assumptions for reliable anomaly detection.