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

The task of demixing a balanced two log-concave densities with the same and known covariance matrix seems restrictive. The authors did not discuss whether the results apply to unbalanced mixtures of two log-concave densities, nor did they discuss the implication of requiring covariances for the two being the same or the knowledge of covariances. The works builds on previous works on global convergence guarantees via EM for a balanced 2 GMM (or mixture of 2 truncated Gaussians) with known covariance, as well as following up works on mixture of 2 linear regressions and mixtures of 2 1-d laplacian distributions. The methodological contribution is to modify the M-step. However, the technical difficulty of proving convergence or providing finite-sample analysis compared with previous works is unclear.