There is normally a simple choice made in the form of the covariance matrix to be used with HMMs. Either a diagonal covariance matrix is used, with the underlying assumption that elements of the feature vector are independent, or a full or block-diagonal matrix is used, where all or some of the correlations are explicitly modelled. Unfortunately when using full or block-diagonal covariance matr...

The eigenvalue spectrum of covariance matrices is of central importance to a number of data analysis techniques. Usually the sample covariance matrix is constructed from a limited number of noisy samples. We describe a method of inferring the true eigenvalue spectrum from the sample spectrum. Results of Silverstein which characterise the eigenvalue spectrum of the noise covariance matrix and in...

We study covariance matrix estimation for the case of partially observed random vectors, where different samples contain different subsets of vector coordinates. Each observation is the product of the variable of interest with a $0-1$ Bernoulli random variable. We analyze an unbiased covariance estimator under this model, and derive an error bound that reveals relations between the sub-sampling...

This paper proposes a new covariance matching based technique for blurred image PSF (point spread function) estimation. A patch based image degradation model is proposed for the covariance matching estimation framework. A robust covariance metric which is based on Riemannian manifold is adapted to measure the distance between covariance matrices. The optimal PSF is computed by minimizing the di...

The robust estimation of multivariate location and shape is one of the most challenging problems in statistics and crucial in many application areas. The objective is to find highly efficient, robust, computable and affine equivariant location and covariance matrix estimates. In this paper three different concepts of multivariate sign and rank are considered and their ability to carry informati...

Gaussian mixture model (GMM) techniques are popular for speaker identification. Theoretically, each Gaussian function should have a full covariance matrix. However, the diagonal covariance matrix is usually used because the inverse of diagonal covariance matrix can be easily calculated via expectation maximization (EM) algorithm. This paper proposes a new probabilistic principal component analy...

Abstract: We consider small factor analysis models with one or two factors. Fixing the number of factors, we prove a finiteness result about the covariance matrix parameter space when the size of the covariance matrix increases. According to this result, there exists a distinguished matrix size starting at which one can determine whether a given covariance matrix belongs to the parameter space ...

This paper investigates an error covariance matrix splitting technique for multiuser multiple input and multiple output (MIMO) interference downlink channel. Most of the related work has thus far considered the traditional error covariance matrix which has not been well-shaped for maximizing the system capacity. Thus, we split and propose a new iterative error covariance matrix to mitigate the ...

Given a collection of single-market covariance matrix forecasts for different markets, we describe how to embed them into a global forecast of total risk. We do this by starting with any global covariance matrix forecast that contains information about cross-market correlations, and revising it to agree with the pre-specified submarket matrices, preserving the requirement that a covariance matr...

The major difficulties in estimating a large covariance matrix are the high dimensionality and the positive definiteness constraint. To overcome these difficulties, we propose to apply smoothing-based regularization and utilize the modified Cholesky decomposition of the covariance matrix. In our proposal, the covariance matrix is diagonalized by a lower triangular matrix, whose subdiagonals are...