Bayesian structure learning using dynamic programming and MCMC

TL;DR

This paper introduces a hybrid approach combining dynamic programming and MCMC to improve Bayesian structure learning of DAGs, overcoming previous limitations and achieving faster convergence and better predictive performance.

Contribution

It proposes using DP as a proposal distribution for MCMC, addressing prior limitations and enhancing structure learning efficiency.

Findings

Faster convergence to the posterior compared to other methods

More accurate structure learning results

Higher predictive likelihoods on test data

Abstract

MCMC methods for sampling from the space of DAGs can mix poorly due to the local nature of the proposals that are commonly used. It has been shown that sampling from the space of node orders yields better results [FK03, EW06]. Recently, Koivisto and Sood showed how one can analytically marginalize over orders using dynamic programming (DP) [KS04, Koi06]. Their method computes the exact marginal posterior edge probabilities, thus avoiding the need for MCMC. Unfortunately, there are four drawbacks to the DP technique: it can only use modular priors, it can only compute posteriors over modular features, it is difficult to compute a predictive density, and it takes exponential time and space. We show how to overcome the first three of these problems by using the DP algorithm as a proposal distribution for MCMC in DAG space. We show that this hybrid technique converges to the posterior faster than other methods, resulting in more accurate structure learning and higher predictive likelihoods on test data.