In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a highdimensional setting under the assumption that the process has a sparse representation in a large dictionary of basis functions. Using a matrix regression model, we propose a new methodology for high-dimensiona...

There is a growing need for the ability to specify and generate correlated random variables as primitive inputs to stochastic models. Motivated by this need, several authors have explored the generation of random vectors with specified marginals, together with a specified covariance matrix, through the use of a transformation of a multivariate normal random vector (the NORTA method). A covarian...

Given a probability distribution inRn with general (non-white) covariance, a classical estimator of the covariance matrix is the sample covariance matrix obtained from a sample of N independent points. What is the optimal sample size N = N(n) that guarantees estimation with a fixed accuracy in the operator norm? Suppose the distribution is supported in a centered Euclidean ball of radius O( √ n...

OF THESIS COVARIANCE REGULARIZATION IN MIXTURE OF GAUSSIANS FOR HIGH-DIMENSIONAL IMAGE CLASSIFICATION In high dimensions, it is rare to find a data set large enough to compute a non-singular covariance matrix. This problem is exacerbated when performing clustering using a mixture of Gaussians (MoG) because now each cluster’s covariance matrix is computed from only a subset of the data set makin...

We first describe in a unified way how to compute the covariance matrix from the gray levels of the image. We then experimentally investigate whether or not the computed covariance matrix actually reflects the accuracy of the feature position by doing subpixel correction using variable template matching. We also test if the accuracy of the homography and the fundamental matrix can really be imp...

Shrinkage estimation of the covariance matrix of asset returns was introduced to the finance profession several years ago. Since then, the approach has also received considerable attention in various life science studies, as a remedial measure for covariance matrix estimation with insufficient observations of the underlying variables. The approach is about taking a weighted average of the sampl...

A three-mode covariance matrix contains covariances of N observations (e.g., subject scores) on J variables for K different occasions or conditions. We model such an JK×JK covariance matrix as the sum of a (common) covariance matrix having Candecomp/Parafac form, and a diagonal matrix of unique variances. The Candecomp/Parafac form is a generalization of the two-mode case under the assumption o...

This paper analyzes whether standard covariance matrix tests work when dimensionality is large, and in particular larger than sample size. In the latter case, the singularity of the sample covariance matrix makes likelihood ratio tests degenerate, but other tests based on quadratic forms of sample covariance matrix eigenvalues remain well-defined. We study the consistency property and limiting ...

The covariance matrix plays an important role in statistical inference, yet modeling a covariance matrix is often a difficult task in practice due to its dimensionality and the non-negative definite constraint. In order to model a covariance matrix effectively, it is typically broken down into components based on modeling considerations or mathematical convenience. Decompositions that have rece...