Mixing Time of Metropolis-Hastings for Bayesian Community Detection

Bumeng Zhuo, Chao Gao.

Year: 2021, Volume: 22, Issue: 10, Pages: 1−89


We study the computational complexity of a Metropolis-Hastings algorithm for Bayesian community detection. We first establish a posterior strong consistency result for a natural prior distribution on stochastic block models under the optimal signal-to-noise ratio condition in the literature. We then give a set of conditions that guarantee rapidly mixing of a simple Metropolis-Hastings algorithm. The mixing time analysis is based on a careful study of posterior ratios and a canonical path argument to control the spectral gap of the Markov chain.