Bayesian structure learning using dynamic programming and MCMC
This addresses the challenge of efficient Bayesian structure learning for probabilistic graphical models, though it is incremental as it builds on existing dynamic programming and MCMC methods.
The paper tackled the problem of poor mixing in MCMC methods for sampling from the space of DAGs in Bayesian structure learning by proposing a hybrid technique that uses dynamic programming as a proposal distribution. The result is faster convergence to the posterior, leading to more accurate structure learning and higher predictive likelihoods on test data.
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.