Partial Order MCMC for Structure Discovery in Bayesian Networks
This addresses a computational bottleneck in Bayesian network structure discovery, offering an incremental improvement for researchers in probabilistic graphical models.
The paper tackles the problem of estimating posterior probabilities of structural features in Bayesian networks by introducing a new Markov chain Monte Carlo method that samples from the posterior distribution of partial orders, with analytical and empirical results suggesting it outperforms previous methods.
We present a new Markov chain Monte Carlo method for estimating posterior probabilities of structural features in Bayesian networks. The method draws samples from the posterior distribution of partial orders on the nodes; for each sampled partial order, the conditional probabilities of interest are computed exactly. We give both analytical and empirical results that suggest the superiority of the new method compared to previous methods, which sample either directed acyclic graphs or linear orders on the nodes.