Vidhya S | Searcharxiv

arXiv2026

A Probabilistic Circuit-Induced Pseudo-Metric for Out-of-Distribution Detection

Probabilistic Circuits (PCs) are tractable generative models whose internal nodes encode a hierarchy of probabilistic summaries over different variable scopes. Existing PC-based out-of-distribution (OOD) detection methods ignore this hierarchy, reducing the entire circuit to the scalar likelihood (or its uncertainty) computed at the root. We introduce Hierarchical Likelihood Vector (HLV), a representation whose entries are the likelihoods associated with selected PC nodes and define the Hierarchical Likelihood Distance (HLD), a PC-induced pseudo-metric that compares the probability distributions 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 detection. 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 computed exactly, directly from the trained circuit, yielding an approximate analytic decision threshold. Experiments on tabular and MNIST datasets demonstrate that exploiting the hierarchical probabilistic summaries encoded through the PC improve OOD detection over root-likelihood, uncertainty-, typicality- and kernel-based baselines, while naturally localizing distribution shifts to the PC nodes responsible for the shift.

cs.LG↗

arXiv2026

PAR: Plausibility-aware Amortized Recourse Generation

Algorithmic recourse aims to recommend actionable changes to a factual's attributes that flip an unfavorable model decision while remaining realistic and feasible. We formulate recourse as a Constrained Maximum A-Posteriori (MAP) inference problem under the accepted-class data distribution seeking counterfactuals with high likelihood while respecting other recourse constraints. We present PAR, an amortized approximate inference procedure that generates highly likely recourses efficiently. Recourse likelihood is estimated directly using tractable probabilistic models that admit exact likelihood evaluation and efficient gradient propagation that is useful during training. The recourse generator is trained with the objective of maximizing the likelihood under the accepted-class distribution while minimizing the likelihood under the denied-class distribution and other losses that encode recourse constraints. Furthermore, PAR includes a neighborhood-based conditioning mechanism to promote recourse generation that is customized to a factual. We validate PAR on widely used algorithmic recourse datasets and demonstrate its efficiency in generating recourses that are valid, similar to the factual, sparse, and highly plausible, yielding superior performance over existing state-of-the-art approaches.

cs.LG↗