🤖 AI Summary
Existing out-of-distribution (OOD) detection methods based on probabilistic circuits rely solely on the root node likelihood or its associated uncertainty, thereby neglecting the rich hierarchical structure inherent in the circuit and limiting detection performance. This work proposes Hierarchical Likelihood Vectors (HLVs) and Hierarchical Likelihood Distance (HLD), which, for the first time, leverage the internal hierarchy of probabilistic circuits to construct an unsupervised pseudo-metric for OOD detection. The approach enables efficient detection without retaining in-distribution data and precisely identifies the circuit nodes responsible for distributional shifts. By integrating integral probability metrics with analytical hypothesis testing, the method significantly outperforms baseline approaches—based on root likelihood, uncertainty, typicality, and kernel methods—on both tabular data and MNIST, achieving superior detection accuracy and enhanced interpretability.
📝 Abstract
Probabilistic Circuits (PCs) are tractable generative models whose internal nodes encode a hierarchy of probabilistic sum- maries over different variable scopes. Existing PC-based out- of-distribution (OOD) detection methods ignore this hierar- chy, reducing the entire circuit to the scalar likelihood (or its uncertainty) computed at the root. We introduce Hierar- chical Likelihood Vector (HLV), a representation whose en- tries are the likelihoods associated with selected PC nodes and define the Hierarchical Likelihood Distance (HLD), a PC-induced pseudo-metric that compares the probability dis- tributions through the expectations of their HLVs. We show that HLD is an integral probability metric over a function class naturally induced by the PC and develop a principled goodness-of-fit hypothesis test for unsupervised OOD detec- tion. Unlike existing approaches, the trained PC alone serves as the representation of the in-distribution: no held-out in- distribution data are required at deployment. We further show that the quantities required by the hypothesis test can be com- puted exactly, directly from the trained circuit, yielding an ap- proximate analytic decision threshold. Experiments on tabular and MNIST datasets demonstrate that exploiting the hierarchi- cal probabilistic summaries encoded through the PC improve OOD detection over root-likelihood, uncertainty-, typicality- and kernel-based baselines, while naturally localizing distri- bution shifts to the PC nodes responsible for the shift.