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Convergence of Gradient EM on Multi-component Mixture of Gaussians
Bowei Yan · Mingzhang Yin · Purnamrita Sarkar

Wed Dec 06 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #219

In this paper, we study convergence properties of the gradient variant of Expectation-Maximization algorithm~\cite{lange1995gradient} for Gaussian Mixture Models for arbitrary number of clusters and mixing coefficients. We derive the convergence rate depending on the mixing coefficients, minimum and maximum pairwise distances between the true centers, dimensionality and number of components; and obtain a near-optimal local contraction radius. While there have been some recent notable works that derive local convergence rates for EM in the two symmetric mixture of Gaussians, in the more general case, the derivations need structurally different and non-trivial arguments. We use recent tools from learning theory and empirical processes to achieve our theoretical results.

Author Information

Bowei Yan (Jump Trading)
Mingzhang Yin (University of Texas at Austin)
Purnamrita Sarkar (UT Austin)

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