High Dimensional Expectation-Maximization Algorithm: Statistical Optimization and Asymptotic Normality

Understand

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.