Point Estimation of Networks from Posterior Samples

Oregon Convention Center 

Bayesian networks are a method of modeling conditional dependencies among variables and have a wide variety of applications. Bayesian network models place a prior distribution on the network structure, and Markov chain Monte Carlo is typically used for model fitting, which results in thousands of networks sampled from the posterior distribution. Based on these samples, we propose a method to provide a point estimate of a Bayesian network structure. First, we introduce generalized structural Hamming (GSH) loss, a function between the adjacency matrices of networks which satisfies quasi-metric properties. We also introduce a stochastic sweetening algorithm to obtain a Bayes estimate by minimizing the Monte Carlo estimate of the posterior expected GSH loss using the available samples. We provide an investigation of existing methods and our proposed methods. Our loss function and search algorithm are implemented in an R package.

Bayesian estimation


graph estimation

loss functions

Markov chain Monte Carlo

network estimation 

Section on Bayesian Statistical Science