How to Marginalize in Causal Structure Learning?
This work addresses a bottleneck in causal structure learning for researchers and practitioners using Bayesian networks, representing an incremental improvement with a novel method for a known limitation.
The paper tackles the challenge of marginalizing over probability distributions in Bayesian network structure learning by introducing a method using tractable probabilistic circuits, which improves performance compared to existing dynamic programming approaches.
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.