Computing Posterior Probabilities of Structural Features in Bayesian Networks

TL;DR

This paper introduces an efficient algorithm for computing exact posterior probabilities of subnetworks in Bayesian networks, accommodating general priors and scaling to networks with up to 20 variables.

Contribution

It presents a novel algorithm that computes exact posterior probabilities in exponential time with respect to the number of variables, supporting general structure priors.

Findings

Algorithm computes posterior probabilities in O(3^n) time

Supports general structure priors unlike previous methods

Demonstrated on datasets with up to 20 variables

Abstract

We study the problem of learning Bayesian network structures from data. Koivisto and Sood (2004) and Koivisto (2006) presented algorithms that can compute the exact marginal posterior probability of a subnetwork, e.g., a single edge, in O(n2n) time and the posterior probabilities for all n(n-1) potential edges in O(n2n) total time, assuming that the number of parents per node or the indegree is bounded by a constant. One main drawback of their algorithms is the requirement of a special structure prior that is non uniform and does not respect Markov equivalence. In this paper, we develop an algorithm that can compute the exact posterior probability of a subnetwork in O(3n) time and the posterior probabilities for all n(n-1) potential edges in O(n3n) total time. Our algorithm also assumes a bounded indegree but allows general structure priors. We demonstrate the applicability of the algorithm on several data sets with up to 20 variables.