Global Convergence of Least Squares EM for Demixing Two Log-Concave Densities

One important problem in statistics and machine learning is to learn a finite mixture of distributions [18, 24]. In the parametric setting where the functional form of the distribution is known, this problem is to estimate parameters (e.g., mean and covariance) that specify the distribution of each mixture component. The parameter estimation problem for mixture models is inherently nonconvex, posing challenges for both computation and analysis. While many algorithms have been proposed, rigorous performance guarantees are often elusive. One exception is the Gaussian Mixture Model (GMM), for which much theoretical progress has been made in recent years. The goal of this paper is to study algorithmic guarantees for a much broader class of mixture models, namely log-concave distributions.