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Recently, a general method for analyzing the statistical accuracy of the EMalgorithm has been developed and applied to some simple latent variable models[Balakrishnan et al. 2016]. In that method, the basin of attraction for validinitialization is required to be a ball around the truth. Using Stein's Lemma,we extend these results in the case of estimating the centers of atwo-component Gaussian mixture in $d$ dimensions. In particular, wesignificantly expand the basin of attraction to be the intersection of a halfspace and a ball around the origin. If the signal-to-noise ratio is at least aconstant multiple of $ \sqrt{d\log d} $, we show that a random initializationstrategy is feasible.

Statistical Guarantees for Estimating the Centers of a Two-component Gaussian Mixture by EM