Parallel Sampling for Efficient High-dimensional Bayesian Network Structure Learning

TL;DR

This paper introduces PS-MINOBS, a parallel sampling algorithm for high-dimensional Bayesian network structure learning that improves efficiency and score quality over existing methods like MINOBS.

Contribution

The paper presents PS-MINOBS, an extension of MINOBS that uses parallel sampling of Candidate Parent Sets based on a half-normal distribution assumption, enhancing scalability and accuracy.

Findings

PS-MINOBS discovers higher score structures than MINOBS within the same runtime.

Parallel sampling significantly improves computational efficiency.

The method effectively handles high-dimensional data in Bayesian network learning.

Abstract

Score-based algorithms that learn the structure of Bayesian networks can be used for both exact and approximate solutions. While approximate learning scales better with the number of variables, it can be computationally expensive in the presence of high dimensional data. This paper describes an approximate algorithm that performs parallel sampling on Candidate Parent Sets (CPSs), and can be viewed as an extension of MINOBS which is a state-of-the-art algorithm for structure learning from high dimensional data. The modified algorithm, which we call Parallel Sampling MINOBS (PS-MINOBS), constructs the graph by sampling CPSs for each variable. Sampling is performed in parallel under the assumption the distribution of CPSs is half-normal when ordered by Bayesian score for each variable. Sampling from a half-normal distribution ensures that the CPSs sampled are likely to be those which produce the higher scores. Empirical results show that, in most cases, the proposed algorithm discovers higher score structures than MINOBS when both algorithms are restricted to the same runtime limit.