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The Expectation-Maximization algorithm is perhaps the most broadly used algorithm for inference of latent variable problems. A theoretical understanding of its performance, however, largely remains lacking. Recent results established that…

The Gaussian mixture model (GMM) provides a simple yet principled framework for clustering, with properties suitable for statistical inference. In this paper, we propose a new model-based clustering algorithm, called EGMM (evidential GMM),…

This paper tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (EM) algorithm for Gaussian mixture models, has shown interesting properties when…

We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions.…

Gaussian Mixture Models are a powerful tool in Data Science and Statistics that are mainly used for clustering and density approximation. The task of estimating the model parameters is in practice often solved by the Expectation…

Gaussian mixture models (GMMs) are fundamental statistical tools for modeling heterogeneous data. Due to the nonconcavity of the likelihood function, the Expectation-Maximization (EM) algorithm is widely used for parameter estimation of…

Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical…

We propose a novel exponentially-modified Gaussian (EMG) mixture residual model. The EMG mixture is well suited to model residuals that are contaminated by a distribution with positive support. This is in contrast to commonly used robust…

Finite mixture models are among the most popular statistical models used in different data science disciplines. Despite their broad applicability, inference under these models typically leads to computationally challenging non-convex…

The Expectation-Maximization (EM) algorithm is one of the most popular methods used to solve the problem of parametric distribution-based clustering in unsupervised learning. In this paper, we propose to analyze a generalized EM (GEM)…

We investigated the use of Empirical Mode Decomposition (EMD) combined with Gaussian Mixture Models (GMM), feature engineering and machine learning algorithms to optimize trading decisions. We used five, two, and one year samples of hourly…

Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…

We study the convergence behavior of the Expectation Maximization (EM) algorithm on Gaussian mixture models with an arbitrary number of mixture components and mixing weights. We show that as long as the means of the components are separated…

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…

In data-mining applications, we are frequently faced with a large fraction of missing entries in the data matrix, which is problematic for most discriminant machine learning algorithms. A solution that we explore in this paper is the use of…

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…

Modelling highly multi-modal data is a challenging problem in machine learning. Most algorithms are based on maximizing the likelihood, which corresponds to the M(oment)-projection of the data distribution to the model distribution. The…

Finite Mixture of Regressions (FMR) models are among the most widely used approaches in dealing with the heterogeneity among the observations in regression problems. One of the limitations of current approaches is their inability to…

The expectation-maximization (EM) algorithm is an iterative method for finding maximum likelihood estimates when data are incomplete or are treated as being incomplete. The EM algorithm and its variants are commonly used for parameter…

This paper is concerned with an important issue in finite mixture modelling, the selection of the number of mixing components. We propose a new penalized likelihood method for model selection of finite multivariate Gaussian mixture models.…