Related papers: Estimation of Gaussian mixtures in small sample st…

We consider the problem of estimation of a covariance matrix for Gaussian data in a high dimensional setting. Existing approaches include maximum likelihood estimation under a pre-specified sparsity pattern, l_1-penalized loglikelihood…

Gaussian Mixture models (GMMs) are a powerful tool for clustering, classification and density estimation when clustering structures are embedded in the data. The presence of missing values can largely impact the GMMs estimation process,…

We consider the problem of sparse estimation via a lasso-type penalized likelihood procedure in a factor analysis model. Typically, the model estimation is done under the assumption that the common factors are orthogonal (uncorrelated).…

The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…

We propose a new and computationally efficient algorithm for maximizing the observed log-likelihood for a multivariate normal data matrix with missing values. We show that our procedure based on iteratively regressing the missing on the…

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),…

We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…

The classical Gaussian mixture model assumes homogeneity within clusters, an assumption that often fails in real-world data where observations naturally exhibit varying scales or intensities. To address this, we introduce the…

Bayesian nonparametric mixture models are widely used to cluster observations. However, one major drawback of the approach is that the estimated partition often presents unbalanced clusters' frequencies with only a few dominating clusters…

Robust clustering of high-dimensional data is an important topic because clusters in real datasets are often heavy-tailed and/or asymmetric. Traditional approaches to model-based clustering often fail for high dimensional data, e.g., due to…

We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…

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…

While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings…

A Gaussian process has been one of the important approaches for emulating computer simulations. However, the stationarity assumption for a Gaussian process and the intractability for large-scale dataset limit its availability in practice.…

This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…

This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the…

We consider the problem of selecting covariates in spatial linear models with Gaussian process errors. Penalized maximum likelihood estimation (PMLE) that enables simultaneous variable selection and parameter estimation is developed and,…

As an effective nonparametric method, empirical likelihood (EL) is appealing in combining estimating equations flexibly and adaptively for incorporating data information. To select important variables and estimating equations in the sparse…

We study Gaussian sparse estimation tasks in Huber's contamination model with a focus on mean estimation, PCA, and linear regression. For each of these tasks, we give the first sample and computationally efficient robust estimators with…

The Expectation-Maximization (EM) algorithm has been predominantly used to approximate the maximum likelihood estimation of the location-scale Gaussian mixtures. However, when the models are over-specified, namely, the chosen number of…