Enhancing Bayesian Network Structural Learning with Monte Carlo Tree Search

TL;DR

This paper introduces MCTS-BN, a novel hybrid algorithm that adapts Monte Carlo Tree Search for Bayesian Network structure learning, improving robustness and performance over traditional methods especially with suboptimal initial orders.

Contribution

It presents a new MCTS-based approach for BN structure learning that integrates heuristic search algorithms to efficiently explore variable orders.

Findings

MCTS-BN outperforms traditional algorithms in various scenarios.

The hybrid approach enhances reliability in large search spaces.

MCTS-BN surpasses gold standard methods with good initial orders.

Abstract

This article presents MCTS-BN, an adaptation of the Monte Carlo Tree Search (MCTS) algorithm for the structural learning of Bayesian Networks (BNs). Initially designed for game tree exploration, MCTS has been repurposed to address the challenge of learning BN structures by exploring the search space of potential ancestral orders in Bayesian Networks. Then, it employs Hill Climbing (HC) to derive a Bayesian Network structure from each order. In large BNs, where the search space for variable orders becomes vast, using completely random orders during the rollout phase is often unreliable and impractical. We adopt a semi-randomized approach to address this challenge by incorporating variable orders obtained from other heuristic search algorithms such as Greedy Equivalent Search (GES), PC, or HC itself. This hybrid strategy mitigates the computational burden and enhances the reliability of the rollout process. Experimental evaluations demonstrate the effectiveness of MCTS-BN in improving BNs generated by traditional structural learning algorithms, exhibiting robust performance even when base algorithm orders are suboptimal and surpassing the gold standard when provided with favorable orders.