Markov Chain Monte Carlo using Tree-Based Priors on Model Structure
This is an incremental improvement for researchers in Bayesian statistics and machine learning, focusing on structure learning in Bayesian networks.
The paper tackles the problem of defining priors on model structure and sampling from the posterior in Bayesian net structure learning, using a framework based on probability trees and Metropolis-Hastings with tree traversal proposals, but results indicate that priors and traversal strategies must be chosen appropriately for success without providing concrete numerical gains.
We present a general framework for defining priors on model structure and sampling from the posterior using the Metropolis-Hastings algorithm. The key idea is that structure priors are defined via a probability tree and that the proposal mechanism for the Metropolis-Hastings algorithm operates by traversing this tree, thereby defining a cheaply computable acceptance probability. We have applied this approach to Bayesian net structure learning using a number of priors and tree traversal strategies. Our results show that these must be chosen appropriately for this approach to be successful.