Computing the covariance matrix of a population of shapes is essential for establishing shape correspondence, identifying shape variation across the population, and building statistical shape models. The covariance matrix is usually computed from a discrete set of points (a.k.a. landmarks) sampled on each shape. The distribution and density of the sampled points thus greatly influence the covar...

Eigenvalues of sample covariance matrices are often used in biometrics. It has been known for several decades that even though the sample covariance matrix is an unbiased estimate of the real covariance matrix [3], the eigenvalues of the sample covariance matrix are biased estimates of the real eigenvalues [6]. This bias is particularly dominant when the number of samples used for estimation is...

This paper presents two realizations of linear quantum systems for covariance assignment corresponding to pure Gaussian states. The first one is called a cascade realization; given any covariance matrix corresponding to a pure Gaussian state, we can construct a cascaded quantum system generating that state. The second one is called a locally dissipative realization; given a covariance matrix co...

Despite the success of Gaussian processes (GPs) in modelling spatial stochastic processes, dealing with large datasets is still challenging. The problem arises by the need to invert a potentially large covariance matrix during inference. In this paper we address the complexity problem by constructing a new stationary covariance function (Mercer kernel) that naturally provides a sparse covarianc...

This paper considers estimating a covariance matrix of p variables from n observations by either banding or tapering the sample covariance matrix, or estimating a banded version of the inverse of the covariance. We show that these estimates are consistent in the operator norm as long as (logp)/n→ 0, and obtain explicit rates. The results are uniform over some fairly natural well-conditioned fam...

Spatial covariance matrix estimation is of great significance in many applications in climatology, econometrics and many other fields with complex data structures involving spatial dependencies. High dimensionality brings new challenges to this problem, and no theoretical optimal estimator has been proved for the spatial high-dimensional covariance matrix. Over the past decade, the method of re...

We present the path-sum formulation for exact statistical inference of marginals on Gaussian graphical models of arbitrary topology. The path-sum formulation gives the covariance between each pair of variables as a branched continued fraction of finite depth and breadth. Our method originates from the closed-form resummation of infinite families of terms of the walk-sum representation of the co...

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 characterize the eigenvalue spectrum of the noise covariance matrix, and...

We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum likelihood estimator of the constrained covariance matrix, under the assumption of multivariate normality. In contrast to previous approaches, this algorithm h...

This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing estimators: the sample covariance matrix and single-index covariance matrix. This method is generally known as shrinkage, and it is standard in decision theory and in empirical Bayesian statistics. Our shrinkage estimator can be seen as a way to account for extra-market covari...