Probabilistic Circuit Networks

Florian Peter Busch, Moritz Willig, Kristian Kersting, Devendra Singh Dhami

Abstract:

As inference in Bayesian networks (BNs) can quickly become intractable, probabilistic circuits (PCs) have been established as the go-to choice for performing tractable inference.
However, modeling with BNs remains popular as their graphical structure closely aligns with the semantics of the problem, making them modular and interpretable.
As this generally does not apply to PCs trained from data, we propose probabilistic circuit networks (PCNs).
PCNs model variables using separate PCs each covering the variable and its parents, so that the marginal distributions can be updated in response to changes upstream.
To this end, an iterative proportional fitting (IPF) procedure can be employed, which remains tractable owing to the tractability properties of PCs.
While the inference procedure of PCNs is only approximate and thus performs worse than BNs w.r.t. accuracy, we experimentally show that PCNs are more sample-efficient than full PCs and remain computationally tractable despite implementing the graphical structure directly.

Keywords: probabilistic circuit, approximate inference, iterative proportional fitting

TLDR: PCNs connect small PCs along a DAG and use IPF to pass marginal updates between them, trading exact inference for tractability and sample efficiency

Submission Number: 26