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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

Estimators derived from a divergence criterion such as $\varphi-$divergences are generally more robust than the maximum likelihood ones. We are interested in particular in the so-called MD$\varphi$DE, an estimator built using a dual…

Computation · Statistics 2016-06-14 Diaa Al Mohamad , Michel Broniatowski

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 proximal point algorithm, which is a well-known tool for finding minima of convex functions, is generalized from the classical Hilbert space framework into a nonlinear setting, namely, geodesic metric spaces of nonpositive curvature. We…

Optimization and Control · Mathematics 2012-07-02 Miroslav Bacak

In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the…

Computation · Statistics 2017-03-02 Olivier Cappé , Eric Moulines

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

Clustering is a fundamental task in machine learning and data analysis, but it frequently fails to provide fair representation for various marginalized communities defined by multiple protected attributes -- a shortcoming often caused by…

Machine Learning · Computer Science 2025-11-17 Diptarka Chakraborty , Kushagra Chatterjee , Debarati Das , Tien-Long Nguyen

In this paper, we propose a dynamical systems perspective of the Expectation-Maximization (EM) algorithm. More precisely, we can analyze the EM algorithm as a nonlinear state-space dynamical system. The EM algorithm is widely adopted for…

Optimization and Control · Mathematics 2018-10-05 Orlando Romero , Sarthak Chatterjee , Sérgio Pequito

The expectation-maximization (EM) algorithm introduced by Dempster et al in 1977 is a very general method to solve maximum likelihood estimation problems. In this informal report, we review the theory behind EM as well as a number of EM…

Computation · Statistics 2012-09-10 Alexis Roche

The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…

Machine Learning · Statistics 2022-11-15 Hideitsu Hino , Shotaro Akaho , Noboru Murata

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

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

Optimization and Control · Mathematics 2019-10-29 Sulaiman A. Alghunaim , Kun Yuan , Ali H. Sayed

The EM algorithm is a novel numerical method to obtain maximum likelihood estimates and is often used for practical calculations. However, many of maximum likelihood estimation problems are nonconvex, and it is known that the EM algorithm…

Machine Learning · Statistics 2016-08-16 Hideyuki Miyahara , Koji Tsumura

Clustering is an unsupervised learning method that constitutes a cornerstone of an intelligent data analysis process. It is used for the exploration of inter-relationships among a collection of patterns, by organizing them into homogeneous…

Machine Learning · Computer Science 2010-04-13 G. Nathiya , S. C. Punitha , M. Punithavalli

We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…

Numerical Analysis · Computer Science 2019-09-05 Dimitri P. Bertsekas

The paper exposes a non-parametric approach to latent and co-latent modeling of bivariate data, based upon alternating minimization of the Kullback-Leibler divergence (EM algorithm) for complete log-linear models. For categorical data, the…

Methodology · Statistics 2016-03-10 François Bavaud

Expectation maximization (EM) is the default algorithm for fitting probabilistic models with missing or latent variables, yet we lack a full understanding of its non-asymptotic convergence properties. Previous works show results along the…

Machine Learning · Computer Science 2022-03-01 Frederik Kunstner , Raunak Kumar , Mark Schmidt

Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…

Optimization and Control · Mathematics 2019-12-30 Armin Zare , Hesameddin Mohammadi , Neil K. Dhingra , Tryphon T. Georgiou , Mihailo R. Jovanović

Clustering algorithms are a cornerstone of machine learning applications. Recently, a quantum algorithm for clustering based on the k-means algorithm has been proposed by Kerenidis, Landman, Luongo and Prakash. Based on their work, we…

Quantum Physics · Physics 2020-01-23 Hideyuki Miyahara , Kazuyuki Aihara , Wolfgang Lechner

We propose a clustering-based generalized low rank approximation method, which takes advantage of appealing features from both the generalized low rank approximation of matrices (GLRAM) and cluster analysis. It exploits a more general form…

Optimization and Control · Mathematics 2025-02-21 Yujun Zhu , Jie Zhu , Hizba Arshad , Zhongming Wang , Ju Ming