High Dimensional Expectation-Maximization Algorithm: Statistical Optimization and Asymptotic Normality
Year: 2014
Type: article
Abstract: We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estimation. With an appropriate initialization, this algorithm converges at a geometric rate and attains an estimator with the (near-)optimal statistical rate of convergence. (ii) Based on the obtained estimator, we propose new inferential procedures for testing hypotheses and constructing confidence intervals for low dimensional components of high dimensional parameters. For a broad family of statistical models, our framework establishes the first computationally feasible approach for optimal estimation and asymptotic inference in high dimensions. Our theory is supported by thorough numerical results.
Source: PubMed
Authors: Wang, Zhaoran, Gu, Quanquan, Ning, Yang, Liu, Han
Institution: Princeton University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2185602187