Related papers: Manifold Optimization for Gaussian Mixture Models

In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…

The speed of convergence of the Expectation Maximization (EM) algorithm for Gaussian mixture model fitting is known to be dependent on the amount of overlap among the mixture components. In this paper, we study the impact of mixing…

Riemannian optimization is a principled framework for solving optimization problems where the desired optimum is constrained to a smooth manifold $\mathcal{M}$. Algorithms designed in this framework usually require some geometrical…

Non-Gaussian and multimodal distributions are an important part of many recent robust sensor fusion algorithms. In difference to robust cost functions, they are probabilistically founded and have good convergence properties. Since their…

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…

Mixture of linear regression is well studied in statistics and machine learning, where the data points are generated probabilistically using $k$ linear models. Algorithms like Expectation Maximization (EM) may be used to recover the ground…

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…

This paper integrates manifold learning techniques within a \emph{Gaussian process upper confidence bound} algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of…

Gaussian Process (GP) models are popular statistical surrogates used for emulating computationally expensive computer simulators. The quality of a GP model fit can be assessed by a goodness of fit measure based on optimized likelihood.…

Recovering physical properties of objects in motion is a core task across scientific and industrial applications. When the relative motion between the object and the sensing apparatus provides sufficient angular coverage, Computerized…

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…

This paper investigates Gaussian copula mixture models (GCMM), which are an extension of Gaussian mixture models (GMM) that incorporate copula concepts. The paper presents the mathematical definition of GCMM and explores the properties of…

Channel estimation in quantized systems is challenging, particularly in low-resolution systems. In this work, we propose to leverage a Gaussian mixture model (GMM) as generative prior, capturing the channel distribution of the propagation…

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…

Image restoration has experienced significant advancements due to the development of deep learning. Nevertheless, it encounters challenges related to ill-posed problems, resulting in deviations between single model predictions and…

In this letter, we propose a Gaussian mixture model (GMM)-based channel estimator which is learned on imperfect training data, i.e., the training data are solely comprised of noisy and sparsely allocated pilot observations. In a practical…

Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural images are highly…

We propose an Anderson Acceleration (AA) scheme for the adaptive Expectation-Maximization (EM) algorithm for unsupervised learning a finite mixture model from multivariate data (Figueiredo and Jain 2002). The proposed algorithm is able to…

In this work, we propose variations of a Gaussian mixture model (GMM) based channel estimator that was recently proven to be asymptotically optimal in the minimum mean square error (MMSE) sense. We account for the need of low computational…

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…