Likelihood Maximization and Moment Matching in Low <scp>SNR</scp> Gaussian Mixture Models

نویسندگان

چکیده

We derive an asymptotic expansion for the log-likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in low signal-to-noise regime. The reveals intimate connection between two types algorithms parameter estimation: method moments and likelihood optimizing such as Expectation-Maximization (EM). show that optimization SNR regime reduces to a sequence least squares problems match estimate ground truth one by one. This is stepping stone towards analysis EM maximum estimation wide range models. A motivating application study cryo-electron microscopy data, which can be modeled GMM algebraic constraints imposed on centers. discuss our algebraically constrained GMMs, among other example interest. © 2022 Authors. Communications Pure Applied Mathematics published Wiley Periodicals LLC.

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ژورنال

عنوان ژورنال: Communications on Pure and Applied Mathematics

سال: 2022

ISSN: ['1097-0312', '0010-3640']

DOI: https://doi.org/10.1002/cpa.22051