Exact Structure Discovery in Bayesian Networks with Less Space

TL;DR

This paper introduces new space-efficient algorithms for exact Bayesian network structure discovery, enabling larger networks to be analyzed with reduced memory and improved parallelization, supported by empirical evaluation.

Contribution

It presents novel space-time tradeoff algorithms for Bayesian network structure discovery, extending the feasible network size and enabling practical parallelization.

Findings

Achieves structure discovery with reduced space requirements.

Provides algorithms with improved time complexity under space constraints.

Demonstrates empirical potential of the proposed methods.

Abstract

The fastest known exact algorithms for scorebased structure discovery in Bayesian networks on n nodes run in time and space 2nnO(1). The usage of these algorithms is limited to networks on at most around 25 nodes mainly due to the space requirement. Here, we study space-time tradeoffs for finding an optimal network structure. When little space is available, we apply the Gurevich-Shelah recurrence-originally proposed for the Hamiltonian path problem-and obtain time 22n-snO(1) in space 2snO(1) for any s = n/2, n/4, n/8, . . .; we assume the indegree of each node is bounded by a constant. For the more practical setting with moderate amounts of space, we present a novel scheme. It yields running time 2n(3/2)pnO(1) in space 2n(3/4)pnO(1) for any p = 0, 1, . . ., n/2; these bounds hold as long as the indegrees are at most 0.238n. Furthermore, the latter scheme allows easy and efficient parallelization beyond previous algorithms. We also explore empirically the potential of the presented techniques.