Global Convergence of EM Algorithm for Mixtures of Two Component Linear Regression
CoRR(2018)
摘要
The Expectation-Maximization algorithm is perhaps the most broadly used
algorithm for inference of latent variable problems. A theoretical
understanding of its performance, however, largely remains lacking. Recent
results established that EM enjoys global convergence for Gaussian Mixture
Models. For Mixed Linear Regression, however, only local convergence results
have been established, and those only for the high SNR regime. We show here
that EM converges for mixed linear regression with two components (it is known
that it may fail to converge for three or more), and moreover that this
convergence holds for random initialization. Our analysis reveals that EM
exhibits very different behavior in Mixed Linear Regression from its behavior
in Gaussian Mixture Models, and hence our proofs require the development of
several new ideas.
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关键词
em algorithm,mixtures
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