How to Marginalize in Causal Structure Learning?

TL;DR

This paper introduces a novel approach using probabilistic circuits for efficient and exact marginalization in Bayesian network structure learning, enhancing the accuracy of inferred structures from data.

Contribution

The paper proposes a new method employing probabilistic circuits to perform marginalization without restrictions, improving Bayesian structure learning.

Findings

Improved accuracy in structure learning results.

Faster marginalization computations.

Enhanced performance over existing methods.

Abstract

Bayesian networks (BNs) are a widely used class of probabilistic graphical models employed in numerous application domains. However, inferring the network's graphical structure from data remains challenging. Bayesian structure learners approach this problem by inferring a posterior distribution over the possible directed acyclic graphs underlying the BN. The inference process often requires marginalizing over probability distributions, which is typically done using dynamic programming methods that restrict the set of possible parents for each node. Instead, we present a novel method that utilizes tractable probabilistic circuits to circumvent this restriction. This method utilizes a new learning routine that trains these circuits on both the original distribution and marginal queries. The architecture of probabilistic circuits then inherently allows for fast and exact marginalization on the learned distribution. We then show empirically that utilizing our method to answer marginals allows Bayesian structure learners to improve their performance compared to current methods.