MLE and EM for Well-Separated Mixtures: Minimax Rates


The Expectation-Maximization (EM) algorithm is a widely used tool for computing maximum likelihood estimator (MLE) in statistical inference with latent variables. Since the seminal work by Balakrishnan et al., recent line of work established non-asymptotic convergence guarantees of the EM algorithm under various statistical and regularity assumptions. In this work, we revisit the framework established in Balakrishnan et al., enlarging the scope to a general $K$ mixture of distributions with an unified framework.