Local Structure Discovery in Bayesian Networks

TL;DR

This paper introduces SLL, a score-based local learning algorithm for Bayesian networks that focuses on specific target variables, offering a scalable alternative to global structure learning with promising empirical results.

Contribution

The paper presents a novel score-based local learning algorithm, SLL, with theoretical soundness and practical competitiveness, and explores methods for constructing full network structures from local results.

Findings

SLL is competitive with the HITON algorithm.

SLL is theoretically optimal with large samples.

Two algorithms for full network construction from local results are proposed.

Abstract

Learning a Bayesian network structure from data is an NP-hard problem and thus exact algorithms are feasible only for small data sets. Therefore, network structures for larger networks are usually learned with various heuristics. Another approach to scaling up the structure learning is local learning. In local learning, the modeler has one or more target variables that are of special interest; he wants to learn the structure near the target variables and is not interested in the rest of the variables. In this paper, we present a score-based local learning algorithm called SLL. We conjecture that our algorithm is theoretically sound in the sense that it is optimal in the limit of large sample size. Empirical results suggest that SLL is competitive when compared to the constraint-based HITON algorithm. We also study the prospects of constructing the network structure for the whole node set based on local results by presenting two algorithms and comparing them to several heuristics.