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- W4287751444 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 toward 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." @default.
- W4287751444 created "2022-07-26" @default.
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- W4287751444 date "2020-06-26" @default.
- W4287751444 modified "2023-09-29" @default.
- W4287751444 title "Likelihood Maximization and Moment Matching in Low SNR Gaussian Mixture Models" @default.
- W4287751444 doi "https://doi.org/10.48550/arxiv.2006.15202" @default.
- W4287751444 hasPublicationYear "2020" @default.
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