Partitioned hybrid learning of Bayesian network structures

TL;DR

This paper introduces a novel hybrid approach for Bayesian network structure learning, combining three algorithms to improve efficiency and accuracy, validated through theoretical guarantees and extensive empirical comparisons.

Contribution

The paper presents a new hybrid method called pHGS with three algorithms that enhance structure learning efficiency and accuracy, supported by theoretical and empirical validation.

Findings

Significant computational reductions over PC algorithm

High structural accuracy with HGI strategy

Superior performance compared to state-of-the-art algorithms

Abstract

We develop a novel hybrid method for Bayesian network structure learning called partitioned hybrid greedy search (pHGS), composed of three distinct yet compatible new algorithms: Partitioned PC (pPC) accelerates skeleton learning via a divide-and-conquer strategy, $p$-value adjacency thresholding (PATH) effectively accomplishes parameter tuning with a single execution, and hybrid greedy initialization (HGI) maximally utilizes constraint-based information to obtain a high-scoring and well-performing initial graph for greedy search. We establish structure learning consistency of our algorithms in the large-sample limit, and empirically validate our methods individually and collectively through extensive numerical comparisons. The combined merits of pPC and PATH achieve significant computational reductions compared to the PC algorithm without sacrificing the accuracy of estimated structures, and our generally applicable HGI strategy reliably improves the estimation structural accuracy of popular hybrid algorithms with negligible additional computational expense. Our empirical results demonstrate the superior empirical performance of pHGS against many state-of-the-art structure learning algorithms.