Membership Circuits: Tractable Membership Testing via Probabilistic Circuits

Statistical hypothesis testing is a cornerstone of scientific progress, yet rigorous methods for high-dimensional data remain scarce. This gap severely limits reliable statistical inference in critical domains such as medicine and pharmaceutics. We address this limitation by introducing Membership Circuits (MCs), a model that leverages the structural properties of Probabilistic Circuits (PCs) to enable tractable, i.e., exact and efficient, computation of multivariate $p$-values, providing formal guarantees on the membership hypothesis. We present extensive evaluations of the test’s properties and investigate its effectiveness in out-of-distribution (OOD) detection. Finally, we demonstrate that MCs are aware if the learned architecture fails to capture the original dataset.