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Activity Number: 28 - Advances in Bayesian Theory and Methods on Network Data Modeling
Type: Topic Contributed
Date/Time: Monday, August 3, 2020 : 10:00 AM to 11:50 AM
Sponsor: Section on Bayesian Statistical Science
Abstract #310926
Title: Optimal Bayesian Estimation for Low-Rank Random Graphs
Author(s): Fangzheng Xie* and Yanxun Xu
Companies: Johns Hopkins University and Johns Hopkins University
Keywords: Likelihood-based graph estimation; Minimax-optimality; Posterior spectral embedding

Random graph models have been a heated topic in statistics and machine learning, as well as a broad range of application areas. In this work, we focus on a class of low-rank random graph models, namely, the random dot product graphs. We propose a Bayesian approach, called the posterior spectral embedding, for estimating the latent positions, and prove its optimality. Unlike the classical spectral-based methods, the posterior spectral embedding is a fully likelihood-based graph estimation method taking advantage of the likelihood information of the graph model. A minimax lower bound for estimating the latent positions is established, and we show that the posterior spectral embedding achieves this lower bound in the following two senses: the posterior contraction rate is minimax-optimal, and it produces a point estimator achieving the minimax lower bound asymptotically. The practical performance of the proposed methodology is illustrated through extensive synthetic examples and the analysis of a Wikipedia network data.

Authors who are presenting talks have a * after their name.

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