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

arXiv1906.06776MaRDI QIDQ6320581

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Publication date: 16 June 2019

Abstract: 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. 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 distribution. Moreover, we show that this global convergence property is robust under model mis-specification. Our analysis generalizes previous techniques for proving the convergence results for Gaussian mixtures. In particular, we make use of an angle-decreasing property for establishing global convergence of Least Squares EM beyond Gaussian settings, as $el{l}_2$ distance contraction no longer holds globally for general log-concave mixtures.

Has companion code repository: https://github.com/weiiew28/Least-Squares-EM

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