Maximum Likelihood Estimation and Expectation-Maximization for a Mixture of Log-Concave Densities with Separation


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 log-concave distributions with an unified framework.