面向分布外检测的概率电路诱导伪度量
A Probabilistic Circuit-Induced Pseudo-Metric for Out-of-Distribution Detection
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中文总结 AI 辅助
该研究提出基于概率电路（PC）的层次似然距离（HLD）与层次似然向量（HLV），用于无监督分布外检测，无需保留分布内数据，在表格及MNIST数据集上的检测性能优于多种基线方法，还可定位分布偏移对应的PC节点。
中文摘要 AI 辅助
概率电路（Probabilistic Circuits, PCs）是可处理的生成模型，其内部节点编码了不同变量作用域上的概率摘要层次结构。现有基于PC的分布外（Out-of-Distribution, OOD）检测方法忽略了该层次结构，将整个电路简化为根节点处计算的标量似然（或其不确定性）。本文提出层次似然向量（Hierarchical Likelihood Vector, HLV），其元素为与选定PC节点关联的似然；并定义层次似然距离（Hierarchical Likelihood Distance, HLD），这是一种由PC诱导的伪度量，通过比较两个分布的HLV期望来实现分布对比。我们证明HLD是PC自然诱导的函数类上的积分概率度量，并开发了用于无监督OOD检测的原则性拟合优度假设检验。与现有方法不同，部署时仅需训练好的PC即可作为分布内的表示，无需保留分布内数据。我们进一步表明，假设检验所需的量可直接从训练好的电路精确计算，从而得到近似的解析决策阈值。在表格数据和MNIST数据集上的实验表明，利用PC编码的层次概率摘要，相比根似然、不确定性、典型性和基于核的基线方法，可提升OOD检测性能，同时能自然地将分布偏移定位到负责该偏移的PC节点。
英文摘要
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.
