Point Estimation of Networks from Posterior Samples
Abstract Number:
3747
Submission Type:
Contributed Abstract
Contributed Abstract Type:
Paper
Participants:
David Dahl (1), Elissa Bailey (1), Jacob Andros (2)
Institutions:
(1) Brigham Young University, Provo, UT, (2) Texas A&M University, College Station, TX
Co-Author(s):
First Author:
Presenting Author:
Abstract Text:
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.
Keywords:
Bayesian estimation
|graph estimation|loss functions|Markov chain Monte Carlo|network estimation|
Sponsors:
Section on Bayesian Statistical Science
Tracks:
Bayesian nonparametrics
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