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

Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)

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Wei Qian, Yuqian Zhang, Yudong Chen


This work studies the location estimation problem for a mixture of two rotation invariant log-concave densities. We demonstrate that Least Squares EM, a variant of the EM algorithm, converges to the true location parameter from a randomly initialized point. Moreover, we establish the explicit convergence rates and sample complexity bounds, revealing their dependence on the signal-to-noise ratio and the tail property of the log-concave distributions. Our analysis generalizes previous techniques for proving the convergence results of Gaussian mixtures, and highlights that an angle-decreasing property is sufficient for establishing global convergence for Least Squares EM.