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In this paper, we outline the use of Mixture Models in density estimation of large astronomical databases. This method of density estimation has been known in Statistics for some time but has not been implemented because of the large…
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.…
This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs), which enables accurate quantification of both epistemic and aleatoric uncertainty. By assuming the data generating process…
Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covariance matrices in high-dimensional spaces, spherical GMMs…
Unlike their conventional use as estimators of probability density functions in reinforcement learning (RL), this paper introduces a novel function-approximation role for Gaussian mixture models (GMMs) as direct surrogates for Q-function…
This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of clusters of the involved covariance matrices according to a criterion, such as sharing Principal…
In robotic inspection of aviation parts, achieving accurate pairwise point cloud registration between scanned and model data is essential. However, noise and outliers generated in robotic scanned data can compromise registration accuracy.…
Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…
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…
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…
Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…
The Expectation-Maximisation (EM) algorithm is a central tool in statistics and machine learning, widely used for latent-variable models such as Gaussian Mixture Models (GMMs). Despite its ubiquity, EM is typically treated as a…
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…
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…
Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…
When constructing a Bayesian Machine Learning model, we might be faced with multiple different prior distributions and thus are required to properly consider them in a sensible manner in our model. While this situation is reasonably well…
Cluster analysis faces two problems in high dimensions: first, the `curse of dimensionality' that can lead to overfitting and poor generalization performance; and second, the sheer time taken for conventional algorithms to process large…
Data which lie in the space $\mathcal{P}_{m\,}$, of $m \times m$ symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications including medical imaging, computer vision, and radar signal…
This paper uses sample data to study the problem of comparing populations on finite-dimensional parallelizable Riemannian manifolds and more general trivial vector bundles. Utilizing triviality, our framework represents populations as…
A new Riemannian geometry for the Compound Gaussian distribution is proposed. In particular, the Fisher information metric is obtained, along with corresponding geodesics and distance function. This new geometry is applied on a change…