AI summaryⓘ
The authors study a kind of model called Probabilistic Circuits (PCs) which organize the likelihood of data in a hierarchical way. They propose a new method to detect when new data is different from what the model expects (out-of-distribution detection) by using a vector of likelihoods from different parts of the PC, rather than just a single likelihood number at the root. This new method, along with a way to measure differences between distributions called Hierarchical Likelihood Distance (HLD), allows the authors to perform tests for detecting unusual data without needing extra validation data. Their experiments show this hierarchical approach is better at finding anomalies and can identify where in the model the differences occur.
Probabilistic CircuitsOut-of-Distribution DetectionLikelihoodHierarchical ModelsHypothesis TestingIntegral Probability MetricGenerative ModelsGoodness-of-FitDistribution Shift
Authors
Bhumika K, Vidhya S, Narayanan C Krishnan
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.