Faster Perfect Sampling of Bayesian Network Structures

Juha Harviainen, Mikko Koivisto

Keywords: Bayesian networks, perfect sampling, rejection sampling, structure learning

TL;DR: We present a faster algorithm for generating Bayesian network structures exactly from the posterior distribution by utilizing rejection sampling.

Abstract: Bayesian inference of a Bayesian network structure amounts to averaging over directed acyclic graphs (DAGs) on a given set of $n$ variables, each DAG weighted by its posterior probability. In practice, save some special inference tasks, one averages over a sample of DAGs generated perfectly or approximately from the posterior. For the hard problem of perfect sampling, we give an algorithm that runs in $O(2.829^n)$ expected time, getting below $O(3^n)$ for the first time. Our algorithm reduces the problem into two smaller sampling problems whose outputs are combined; followed by a simple rejection step, perfect samples are obtained. Subsequent samples can be generated considerably faster. Empirically, we observe speedups of several orders of magnitude over the state of the art.

List Of Authors: Harviainen, Juha and Koivisto, Mikko

Submission Number: 386