On Priors in Bayesian Probabilistic Circuits and Multivariate Pólya Trees

Martin Trapp, Arno Solin

Keywords: Probabilistic Circuits, Polya trees, Bayesian nonparametrics

Abstract: Bayesian formulations of probabilistic circuits (PCs) have gained increasing attention, e.g., to regularize parameter or structure learning or perform model selection. However, prior specification, an essential part of the Bayesian workflow, is often not adequately addressed. In this work, we discuss priors in Bayesian PCs and show that certain constructions are related to Pólya tree processes in the limit of infinite depth. Furthermore, we show that Bayesian PCs can accurately represent mixtures of multivariate Pólya trees with only a fraction of the random variables required in the former. We verify our findings with simulations on synthetic data.