Likelihood Maximization and Moment Matching in Low SNR Gaussian Mixture Models
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2023-04
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Journal Article
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yes
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Abstract
We derive an asymptotic expansion for the log-likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for parameter estimation: the method of moments and likelihood optimizing algorithms such as Expectation-Maximization (EM). We show that likelihood optimization in the low SNR regime reduces to a sequence of least squares optimization problems that match the moments of the estimate to the ground truth moments one by one. This connection is a stepping stone towards the analysis of EM and maximum likelihood estimation in a wide range of models. A motivating application for the study of low SNR mixture models is cryo-electron microscopy data, which can be modeled as a GMM with algebraic constraints imposed on the mixture centers. We discuss the application of our expansion to algebraically constrained GMMs, among other example models of interest.
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76 (4)
Pages / Article No.
788 - 842
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Wiley
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09679 - Bandeira, Afonso / Bandeira, Afonso
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Is new version of: http://hdl.handle.net/20.500.11850/465563