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We present a family of \textit{Gaussian Mixture Approximation} (GMA) samplers for sampling unnormalised target densities, encompassing \textit{weights-only GMA} (W-GMA), \textit{Laplace Mixture Approximation} (LMA),…
We study modeling and inference with the Elliptical Gamma Distribution (EGD). We consider maximum likelihood (ML) estimation for EGD scatter matrices, a task for which we develop new fixed-point algorithms. Our algorithms are efficient and…
Finite mixture models have become a popular tool for clustering. Amongst other uses, they have been applied for clustering longitudinal data and clustering high-dimensional data. In the latter case, a latent Gaussian mixture model is…
Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…
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…
Motivated by applications in machine learning and statistics, we study distributed optimization problems over a network of processors, where the goal is to optimize a global objective composed of a sum of local functions. In these problems,…
Determining the optimal number and identity of structural clusters from an ensemble of molecular configurations continues to be a challenge. Recent structural clustering methods have focused on the use of internal coordinates due to the…
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…
In this paper we provide a new analysis of the SEM algorithm. Unlike previous work, we focus on the analysis of a single run of the algorithm. First, we discuss the algorithm for general mixture distributions. Second, we consider Gaussian…
The ensemble Gaussian mixture filter combines the simplicity and power of Gaussian mixture models with the provable convergence and power of particle filters. The quality of the ensemble Gaussian mixture filter heavily depends on the choice…
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…
Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering…
Training the parameters of statistical models to describe a given data set is a central task in the field of data mining and machine learning. A very popular and powerful way of parameter estimation is the method of maximum likelihood…
We consider the problem of estimating means of two Gaussians in a 2-Gaussian mixture, which is not balanced and is corrupted by noise of an arbitrary distribution. We present a robust algorithm to estimate the parameters, together with…
This paper introduces a novel mixture model-based approach for simultaneous clustering and optimal segmentation of functional data which are curves presenting regime changes. The proposed model consists in a finite mixture of piecewise…
In this paper, we establish new convergence results for the quantized distributed gradient descent and suggest a novel strategy of choosing the stepsizes for the high-performance of the algorithm. Under the strongly convexity assumption on…
Expectation maximisation (EM) is usually thought of as an unsupervised learning method for estimating the parameters of a mixture distribution, however it can also be used for supervised learning when class labels are available. As such, EM…
A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse…
We analyze the classical EM algorithm for parameter estimation in the symmetric two-component Gaussian mixtures in $d$ dimensions. We show that, even in the absence of any separation between components, provided that the sample size…
Clustering mixtures of Gaussian distributions is a fundamental and challenging problem that is ubiquitous in various high-dimensional data processing tasks. While state-of-the-art work on learning Gaussian mixture models has focused…