Entropic Issues in Likelihood-Based OOD Detection
This provides a theoretical explanation for OOD detection failures in likelihood-based methods, aiding researchers in improving model reliability.
The paper tackles the issue where deep generative models assign higher likelihoods to out-of-distribution (OOD) data than in-distribution data, by decomposing average likelihood into KL divergence and entropy terms, showing that entropy suppresses likelihoods on higher-entropy datasets.
Deep generative models trained by maximum likelihood remain very popular methods for reasoning about data probabilistically. However, it has been observed that they can assign higher likelihoods to out-of-distribution (OOD) data than in-distribution data, thus calling into question the meaning of these likelihood values. In this work we provide a novel perspective on this phenomenon, decomposing the average likelihood into a KL divergence term and an entropy term. We argue that the latter can explain the curious OOD behaviour mentioned above, suppressing likelihood values on datasets with higher entropy. Although our idea is simple, we have not seen it explored yet in the literature. This analysis provides further explanation for the success of OOD detection methods based on likelihood ratios, as the problematic entropy term cancels out in expectation. Finally, we discuss how this observation relates to recent success in OOD detection with manifold-supported models, for which the above decomposition does not hold directly.