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The Expectation-Maximization (EM) algorithm (Dempster, Laird and Rubin, 1977) is a popular method for computing maximum likelihood estimates (MLEs) in problems with missing data. Each iteration of the al- gorithm formally consists of an…

Statistics Theory · Mathematics 2012-06-22 Ronald C. Neath

Expectation maximization (EM) is a technique for estimating maximum-likelihood parameters of a latent variable model given observed data by alternating between taking expectations of sufficient statistics, and maximizing the expected log…

Methodology · Statistics 2018-07-10 Donna Henderson , Gerton Lunter

The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…

Computation · Statistics 2024-01-03 William Ruth

Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing maximum likelihood estimate when dealing with Gaussian Mixture Model (GMM). When the sample size is smaller than the data dimension, this could lead…

Machine Learning · Statistics 2023-07-06 Pierre Houdouin , Matthieu Jonkcheere , Frederic Pascal

Online variants of the Expectation Maximization (EM) algorithm have recently been proposed to perform parameter inference with large data sets or data streams, in independent latent models and in hidden Markov models. Nevertheless, the…

Statistics Theory · Mathematics 2012-06-01 Sylvain Le Corff , Gersende Fort

The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…

Quantum Physics · Physics 2020-07-08 Iordanis Kerenidis , Alessandro Luongo , Anupam Prakash

The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…

Statistics Theory · Mathematics 2017-05-31 Chong Wu , Can Yang , Hongyu Zhao , Ji Zhu

Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian…

Machine Learning · Statistics 2023-03-28 Pierre Houdouin , Esa Ollila , Frederic Pascal

The Expectation-Maximization (EM) algorithm for mixture models often results in slow or invalid convergence. The popular convergence proof affirms that the likelihood increases with Q; Q is increasing in the M -step and non-decreasing in…

Machine Learning · Computer Science 2018-10-29 Chenguang Lu

The expectation-maximization (EM) algorithm is an iterative computational method to calculate the maximum likelihood estimators (MLEs) from the sample data. It converts a complicated one-time calculation for the MLE of the incomplete data…

Computation · Statistics 2016-08-08 Lingyao Meng

The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step…

Statistics Theory · Mathematics 2022-05-03 Thomas Lartigue , Stanley Durrleman , Stéphanie Allassonnière

The EM algorithm is one of the most popular algorithm for inference in latent data models. The original formulation of the EM algorithm does not scale to large data set, because the whole data set is required at each iteration of the…

Machine Learning · Statistics 2019-10-29 Belhal Karimi , Hoi-To Wai , Eric Moulines , Marc Lavielle

Expectation maximisation (EM) is an unsupervised learning method for estimating the parameters of a finite mixture distribution. It works by introducing "hidden" or "latent" variables via Baum's auxiliary function $Q$ that allow the joint…

Machine Learning · Computer Science 2022-05-19 Graham W. Pulford

The Expectation-Maximization (EM) algorithm is a widely used method for maximum likelihood estimation in models with latent variables. For estimating mixtures of Gaussians, its iteration can be viewed as a soft version of the k-means…

Machine Learning · Statistics 2017-06-06 Constantinos Daskalakis , Christos Tzamos , Manolis Zampetakis

The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…

Optimization and Control · Mathematics 2026-02-12 Kensuke Asai , Jun-ya Gotoh

This paper deals with parameter estimation when the data are randomly right censored. The maximum likelihood estimates from censored samples are obtained by using the expectation-maximization (EM) and Monte Carlo EM (MCEM) algorithms. We…

Computation · Statistics 2012-03-20 Chanseok Park , Seong Beom Lee

Inspired from quantum Monte Carlo, by using unbiased estimators all the time and sampling discrete and continuous variables at the same time using Metropolis algorithm, we present a novel, fast, and accurate high performance Monte Carlo…

The Stochastic Approximation EM (SAEM) algorithm, a variant stochastic approximation of EM, is a versatile tool for inference in incomplete data models. In this paper, we review the fundamental EM algorithm and then focus especially on the…

Methodology · Statistics 2018-11-30 Vahid Tadayon

It is known that the estimating equations for quantile regression (QR) can be solved using an EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent…

Methodology · Statistics 2021-08-26 Haim Bar , James Booth , Martin T. Wells

The Expectation Maximization (EM) algorithm is a versatile tool for model parameter estimation in latent data models. When processing large data sets or data stream however, EM becomes intractable since it requires the whole data set to be…

Statistics Theory · Mathematics 2012-10-18 Sylvain Le Corff , Gersende Fort
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