On Pruning for Score-Based Bayesian Network Structure Learning

TL;DR

This paper introduces new theoretical bounds for the BDeu score in Bayesian network structure learning, significantly reducing the search space and improving efficiency in pruning candidate parent sets.

Contribution

The authors derive tighter upper bounds for the BDeu score that outperform previous bounds with minimal additional computational effort.

Findings

New bounds are mathematically proven to be tighter than previous ones.

The bounds significantly improve pruning efficiency in BNSL.

The approach is computationally inexpensive.

Abstract

Many algorithms for score-based Bayesian network structure learning (BNSL), in particular exact ones, take as input a collection of potentially optimal parent sets for each variable in the data. Constructing such collections naively is computationally intensive since the number of parent sets grows exponentially with the number of variables. Thus, pruning techniques are not only desirable but essential. While good pruning rules exist for the Bayesian Information Criterion (BIC), current results for the Bayesian Dirichlet equivalent uniform (BDeu) score reduce the search space very modestly, hampering the use of the (often preferred) BDeu. We derive new non-trivial theoretical upper bounds for the BDeu score that considerably improve on the state-of-the-art. Since the new bounds are mathematically proven to be tighter than previous ones and at little extra computational cost, they are a promising addition to BNSL methods.