A Stochastic Variance-Reduced Coordinate Descent Algorithm for Learning Sparse Bayesian Network from Discrete High-Dimensional Data

TL;DR

This paper introduces a stochastic variance-reduced coordinate descent algorithm for efficiently learning sparse Bayesian networks from high-dimensional discrete data, addressing the large parameter space challenge.

Contribution

It proposes a novel optimization-based method with a variance reduction technique for learning discrete Bayesian networks, improving efficiency and scalability.

Findings

Outperforms existing methods on synthetic benchmark data

Demonstrates high scalability and robustness

Produces high-quality sparse Bayesian network structures

Abstract

This paper addresses the problem of learning a sparse structure Bayesian network from high-dimensional discrete data. Compared to continuous Bayesian networks, learning a discrete Bayesian network is a challenging problem due to the large parameter space. Although many approaches have been developed for learning continuous Bayesian networks, few approaches have been proposed for the discrete ones. In this paper, we address learning Bayesian networks as an optimization problem and propose a score function which guarantees the learnt structure to be a sparse directed acyclic graph. Besides, we implement a block-wised stochastic coordinate descent algorithm to optimize the score function. Specifically, we use a variance reducing method in our optimization algorithm to make the algorithm work efficiently for high-dimensional data. The proposed approach is applied to synthetic data from well-known benchmark networks. The quality, scalability, and robustness of the constructed network are measured. Compared to some competitive approaches, the results reveal that our algorithm outperforms some of the well-known proposed methods.