EcoSta 2022: Start Registration
View Submission - EcoSta2022
A0682
Title: Bayesian sparse Gaussian mixture model in high dimensions Authors:  Yanxun Xu - Johns Hopkins University (United States) [presenting]
Abstract: A Bayesian method is proposed to estimate high-dimensional Gaussian mixture models whose component centers exhibit sparsity using a continuous spike-and-slab shrinkage prior. We establish the minimax risk for parameter estimation in sparse Gaussian mixture models and show that the posterior contraction rate of the proposed Bayesian model is minimax optimal. Computationally, the posterior inference can be implemented via an efficient Gibbs sampler with data augmentation, circumventing the challenging frequentist nonconvex optimization-based algorithms. We also obtain a contraction rate for the misclustering error by using tools from matrix perturbation theory. The validity and usefulness of the proposed approach are demonstrated through simulation studies and the analysis of a single-cell sequencing dataset.