Bayesian structure learning using dynamic programming and MCMC

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.

Appears in Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence (UAI2007)

References in corpus (4)

• Learning the Structure of Dynamic Probabilistic Networks
• A simple approach for finding the globally optimal Bayesian network structure
• Causal Discovery from a Mixture of Experimental and Observational Data
• Finding Optimal Bayesian Networks

Cited by in corpus (5)

• Model-Based Bayesian Reinforcement Learning in Large Structured Domains
• Computing Posterior Probabilities of Structural Features in Bayesian Networks
• Bayesian Model Averaging Using the k-best Bayesian Network Structures
• Spatio-Temporal Graphical Model Selection
• LSBN: A Large-Scale Bayesian Structure Learning Framework for Model Averaging