Pruning Bayesian Networks for Efficient Computation

TL;DR

This paper presents a method for pruning Bayesian networks to reduce computational complexity during inference, especially in multiply connected networks, by preprocessing and constructing minimal equivalent subgraphs.

Contribution

It introduces a preprocessing algorithm to efficiently prune Bayesian networks, minimizing computational effort while preserving inference accuracy, and discusses parallel implementation benefits.

Findings

Pruning can significantly reduce computational complexity in Bayesian networks.

The proposed algorithm constructs minimal equivalent subgraphs with O(e) complexity.

Pruning is especially effective in multiply connected networks.

Abstract

This paper analyzes the circumstances under which Bayesian networks can be pruned in order to reduce computational complexity without altering the computation for variables of interest. Given a problem instance which consists of a query and evidence for a set of nodes in the network, it is possible to delete portions of the network which do not participate in the computation for the query. Savings in computational complexity can be large when the original network is not singly connected. Results analogous to those described in this paper have been derived before [Geiger, Verma, and Pearl 89, Shachter 88] but the implications for reducing complexity of the computations in Bayesian networks have not been stated explicitly. We show how a preprocessing step can be used to prune a Bayesian network prior to using standard algorithms to solve a given problem instance. We also show how our results can be used in a parallel distributed implementation in order to achieve greater savings. We define a computationally equivalent subgraph of a Bayesian network. The algorithm developed in [Geiger, Verma, and Pearl 89] is modified to construct the subgraphs described in this paper with O(e) complexity, where e is the number of edges in the Bayesian network. Finally, we define a minimal computationally equivalent subgraph and prove that the subgraphs described are minimal.