Markov Chain Monte Carlo using Tree-Based Priors on Model Structure

TL;DR

This paper introduces a flexible framework for defining priors on model structures using probability trees and sampling from the posterior with Metropolis-Hastings, applied specifically to Bayesian network structure learning.

Contribution

It proposes a novel tree-based prior framework for model structure and a traversal-based proposal mechanism for efficient sampling in Bayesian network learning.

Findings

Tree-based priors enable flexible structure modeling.

Traversal strategies significantly impact sampling success.

Appropriate prior and traversal choices are crucial for effectiveness.

Abstract

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.