Related papers: Algorithme EM r\'egularis\'e

Mini-batch algorithms have become increasingly popular due to the requirement for solving optimization problems, based on large-scale data sets. Using an existing online expectation-{}-maximization (EM) algorithm framework, we demonstrate…

We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts: a treatment of these algorithms at the population level (in…

We give convergence guarantees for estimating the coefficients of a symmetric mixture of two linear regressions by expectation maximization (EM). In particular, we show that the empirical EM iterates converge to the target parameter vector…

Cluster-weighted modeling (CWM) is a mixture approach for modeling the joint probability of a response variable and a set of explanatory variables. The parameters are estimated by means of the expectation-maximization algorithm according to…

Parameter estimation in logistic regression is a well-studied problem with the Newton-Raphson method being one of the most prominent optimization techniques used in practice. A number of monotone optimization methods including…

This paper studies the problem of estimating the means $\pm\theta_{*}\in\mathbb{R}^{d}$ of a symmetric two-component Gaussian mixture $\delta_{*}\cdot N(\theta_{*},I)+(1-\delta_{*})\cdot N(-\theta_{*},I)$ where the weights $\delta_{*}$ and…

Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare…

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…

We take a new look at parameter estimation for Gaussian Mixture Models (GMMs). In particular, we propose using \emph{Riemannian manifold optimization} as a powerful counterpart to Expectation Maximization (EM). An out-of-the-box invocation…

The expectation--maximization (EM) algorithm combines global monotonicity, local linear convergence, and strong practical robustness, but these features are usually analyzed separately. Global descent is nonlinear, whereas local convergence…

Variance components estimation and mixed model analysis are central themes in statistics with applications in numerous scientific disciplines. Despite the best efforts of generations of statisticians and numerical analysts, maximum…

Clustering and estimating cluster means are core problems in statistics and machine learning, with k-means and Expectation Maximization (EM) being two widely used algorithms. In this work, we provide a theoretical explanation for the…

Mixture Markov Model (MMM) is a widely used tool to cluster sequences of events coming from a finite state-space. However the MMM likelihood being multi-modal, the challenge remains in its maximization. Although Expectation-Maximization…

Evidential-EM (E2M) algorithm is an effective approach for computing maximum likelihood estimations under finite mixture models, especially when there is uncertain information about data. In this paper we present an extension of the E2M…

We investigate convergence of the expectation maximization algorithm by representing it as a generalized proximal method. Convergence of iterates and not just in value is investigated under natural hypotheses such as definability of the…

The stochastic blockmodel (SBM) models the connectivity within and between disjoint subsets of nodes in networks. Prior work demonstrated that the rows of an SBM's adjacency spectral embedding (ASE) and Laplacian spectral embedding (LSE)…

Mixture models of Plackett-Luce (PL) -- one of the most fundamental ranking models -- are an active research area of both theoretical and practical significance. Most previously proposed parameter estimation algorithms instantiate the EM…

Many experiments in medicine and ecology can be conveniently modeled by finite Gaussian mixtures but face the problem of dealing with small data sets. We propose a robust version of the estimator based on self-regression and sparsity…

This paper considers the problem of networks reconstruction from heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well known that parameter estimation in this context is challenging due to large numbers of variables…

Regression analysis with missing data is a long-standing and challenging problem, particularly when there are many missing variables with arbitrary missing patterns. Likelihood-based methods, although theoretically appealing, are often…