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<p>We present a study of the convergence properties of the Expectation-Maximization (EM) algorithm when applied to an overspecified model. In particular, we consider fitting a balanced mixture of two Gaussians to data originating from a single Gaussian. We provide theoretical bounds on the Kullback–Leibler (KL) divergence between the fitted and true distributions. An important feature is concavity and radiality of the expected log-likelihood function on a hypersurface induced by the EM algorithm, which greatly simplifies the analysis. We also show how our result on KL divergence can be used to upperbound the error rate of a mixture discriminant analysis classifier trained by the EM algorithm.</p>

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Convergence of the EM algorithm in KL distance for overspecified Gaussian mixtures

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月19日

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  • Alan Legg,
  • Artur Pak,
  • Igor Melnykov,
  • Arman Bolatov,
  • Zhenisbek Assylbekov

摘要

We present a study of the convergence properties of the Expectation-Maximization (EM) algorithm when applied to an overspecified model. In particular, we consider fitting a balanced mixture of two Gaussians to data originating from a single Gaussian. We provide theoretical bounds on the Kullback–Leibler (KL) divergence between the fitted and true distributions. An important feature is concavity and radiality of the expected log-likelihood function on a hypersurface induced by the EM algorithm, which greatly simplifies the analysis. We also show how our result on KL divergence can be used to upperbound the error rate of a mixture discriminant analysis classifier trained by the EM algorithm.