Related papers: Estimating covariance and precision matrices along…
This paper studies the problem of estimating a covariance matrix from correlated sub-Gaussian samples. We consider using the correlated sample covariance matrix estimator to approximate the true covariance matrix. We establish…
We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…
In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…
We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…
This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is…
We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters $p$ can be much larger than the sample size. We…
Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical…
We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
Finding an approximation of the inverse of the covariance matrix, also known as precision matrix, of a random vector with empirical data is widely discussed in finance and engineering. In data-driven problems, empirical data may be…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…
Cosmological parameter estimation requires that the likelihood function of the data is accurately known. Assuming that cosmological large-scale structure power spectra data are multivariate Gaussian-distributed, we show the accuracy of…
The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in…
This paper deals with the problem of parameter estimation based on certain eigenspaces of the empirical covariance matrix of an observed multidimensional time series, in the case where the time series dimension and the observation window…
In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
We consider the classical problem of estimating the covariance matrix of a subgaussian distribution from i.i.d. samples in the novel context of coarse quantization, i.e., instead of having full knowledge of the samples, they are quantized…
The variance--covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many…
In this paper, we present several estimators of the diagonal elements of the inverse of the covariance matrix, called precision matrix, of a sample of iid random vectors. The focus is on high dimensional vectors having a sparse precision…