Related papers: On the Behavior of the Expectation-Maximization Al…
We study the expectation-maximization (EM) algorithm for general latent-variable models under (i) distributional misspecification and (ii) nonidentifiability induced by a group action. We formulate EM on the quotient parameter space and…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
Normal mean-variance mixture distributions are widely applied to simplify a model's implementation and improve their computational efficiency under the Maximum Likelihood (ML) approach. Especially for distributions with normal mean-variance…
We consider the problem of estimating the parameters a Gaussian Mixture Model with K components of known weights, all with an identity covariance matrix. We make two contributions. First, at the population level, we present a sharper…
This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…
Normal mixture distributions are arguably the most important mixture models, and also the most technically challenging. The likelihood function of the normal mixture model is unbounded based on a set of random samples, unless an artificial…
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…
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…
Pel-recursive motion estimation isa well-established approach. However, in the presence of noise, it becomes an ill-posed problem that requires regularization. In this paper, motion vectors are estimated in an iterative fashion by means of…
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…
Fitts' law is often employed as a predictive model for human movement, especially in the field of human-computer interaction. Models with an assumed Gaussian error structure are usually adequate when applied to data collected from…
In this paper we study the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our first approach discretizes this infinite dimensional convex optimization problem by fixing the support…
Unsupervised learning has been widely used in many real-world applications. One of the simplest and most important unsupervised learning models is the Gaussian mixture model (GMM). In this work, we study the multi-task learning problem on…
In this article, we discuss two specific classes of models - Gaussian Mixture Copula models and Mixture of Factor Analyzers - and the advantages of doing inference with gradient descent using automatic differentiation. Gaussian mixture…
The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the…
We study the convergence of the Expectation-Maximization (EM) algorithm for mixtures of linear regressions with an arbitrary number $k$ of components. We show that as long as signal-to-noise ratio (SNR) is $\tilde{\Omega}(k)$,…
This paper provides a mixture modeling framework using the bivariate generalized exponential distribution. We study different properties of this mixture distribution. Hierarchical EM algorithm is developed for finding the estimates of the…
Spatial generalized linear mixed models (SGLMMs) are popular and flexible models for non-Gaussian spatial data. They are useful for spatial interpolations as well as for fitting regression models that account for spatial dependence, and are…
Learning Gaussian Mixture Models (GMMs) is a fundamental problem in machine learning, with the Expectation-Maximization (EM) algorithm and its popular variant gradient EM being arguably the most widely used algorithms in practice. In the…
Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…