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.
منابع مشابه
Online and Distributed learning of Gaussian mixture models by Bayesian Moment Matching
The Gaussian mixture model is a classic technique for clustering and data modeling that is used in numerous applications. With the rise of big data, there is a need for parameter estimation techniques that can handle streaming data and distribute the computation over several processors. While online variants of the Expectation Maximization (EM) algorithm exist, their data efficiency is reduced ...
متن کاملMaximum likelihood estimation of Gaussian mixture models using stochastic search
Gaussian mixture models (GMM), commonly used in pattern recognition and machine learning, provide a flexible probabilistic model for the data. The conventional expectation–maximization (EM) algorithm for the maximum likelihood estimation of the parameters of GMMs is very sensitive to initialization and easily gets trapped in local maxima. Stochastic search algorithms have been popular alternati...
متن کاملMixture Models and Expectation-Maximization
This tutorial attempts to provide a gentle introduction to EM by way of simple examples involving maximum-likelihood estimation of mixture-model parameters. Readers familiar with ML paramter estimation and clustering may want to skip directly to Sections 5.2 and 5.3.
متن کاملDesign of Gaussian mixture models using matching pursuit
In this paper, a new design algorithm for estimating the parameters of Gaussian Mixture Models is presented. The method is based on the matching pursuit algorithm. Speaker Identification is considered as an application area. The estimated GMM performs as good as the EM algorithm based model. Computational complexity of the proposed method is much lower than the EM algorithm.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2022
ISSN: ['1097-0312', '0010-3640']
DOI: https://doi.org/10.1002/cpa.22051