Why the Counterintuitive Phenomenon of Likelihood Rarely Appears in Tabular Anomaly Detection with Deep Generative Models?

TL;DR

This paper investigates the rarity of the counterintuitive likelihood phenomenon in tabular anomaly detection using deep generative models, showing it is uncommon and proposing a reliable likelihood-based detection approach.

Contribution

It introduces a domain-agnostic formulation to evaluate the phenomenon and demonstrates its rarity in tabular data through extensive experiments and theoretical analysis.

Findings

Counterintuitive likelihood phenomenon is rare in tabular data.

Likelihood-only detection with normalizing flows is practical and reliable.

Data dimensionality and feature correlation influence the phenomenon.

Abstract

Deep generative models with tractable and analytically computable likelihoods, exemplified by normalizing flows, offer an effective basis for anomaly detection through likelihood-based scoring. We demonstrate that, unlike in the image domain where deep generative models frequently assign higher likelihoods to anomalous data, such counterintuitive behavior occurs far less often in tabular settings. We first introduce a domain-agnostic formulation that enables consistent detection and evaluation of the counterintuitive phenomenon, addressing the absence of precise definition. Through extensive experiments on 47 tabular datasets and 10 CV/NLP embedding datasets in ADBench, benchmarked against 13 baseline models, we demonstrate that the phenomenon, as defined, is consistently rare in general tabular data. We further investigate this phenomenon from both theoretical and empirical perspectives, focusing on the roles of data dimensionality and difference in feature correlation. Our results suggest that likelihood-only detection with normalizing flows offers a practical and reliable approach for anomaly detection in tabular domains.