Multi-Domain Sampling With Applications to Structural Inference of Bayesian Networks

TL;DR

This paper introduces a multi-domain sampling method to better understand multimodal posterior distributions, especially in Bayesian network structure learning, by decomposing the space into domains of attraction for more informative summaries.

Contribution

The paper proposes a novel multi-domain sampler that decomposes multimodal distributions into domains of attraction, enhancing structural inference of Bayesian networks from complex data.

Findings

Provides detailed landscape of posterior distributions

Improves accuracy of Bayesian network structure learning

Enhances predictive power of inferred networks

Abstract

When a posterior distribution has multiple modes, unconditional expectations, such as the posterior mean, may not offer informative summaries of the distribution. Motivated by this problem, we propose to decompose the sample space of a multimodal distribution into domains of attraction of local modes. Domain-based representations are defined to summarize the probability masses of and conditional expectations on domains of attraction, which are much more informative than the mean and other unconditional expectations. A computational method, the multi-domain sampler, is developed to construct domain-based representations for an arbitrary multimodal distribution. The multi-domain sampler is applied to structural learning of protein-signaling networks from high-throughput single-cell data, where a signaling network is modeled as a causal Bayesian network. Not only does our method provide a detailed landscape of the posterior distribution but also improves the accuracy and the predictive power of estimated networks.