Related papers: Random Matrix Derived Shrinkage of Spectral Precis…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
This paper introduces a neural network-based nonlinear shrinkage estimator of covariance matrices for the purpose of minimum variance portfolio optimization. It is a hybrid approach that integrates statistical estimation with machine…
In this paper, a new ridge-type shrinkage estimator for the precision matrix has been proposed. The asymptotic optimal shrinkage coefficients and the theoretical loss were derived. Data-driven estimators for the shrinkage coefficients were…
The determination of the covariance matrix and its inverse, the precision matrix, is critical in the statistical analysis of cosmological measurements. The covariance matrix is typically estimated with a limited number of simulations at…
In this paper, we exploit the spiked covariance structure of the clutter plus noise covariance matrix for radar signal processing. Using state-of-the-art techniques high dimensional statistics, we propose a nonlinear shrinkage-based…
One of the major challenges in multivariate analysis is the estimation of population covariance matrix from sample covariance matrix (SCM). Most recent covariance matrix estimators use either shrinkage transformations or asymptotic results…
We address covariance estimation in the sense of minimum mean-squared error (MMSE) for Gaussian samples. Specifically, we consider shrinkage methods which are suitable for high dimensional problems with a small number of samples (large p…
We seek to improve estimates of the power spectrum covariance matrix from a limited number of simulations by employing a novel statistical technique known as shrinkage estimation. The shrinkage technique optimally combines an empirical…
Shrinkage can effectively improve the condition number and accuracy of covariance matrix estimation, especially for low-sample-support applications with the number of training samples smaller than the dimensionality. This paper investigates…
This article studies two regularized robust estimators of scatter matrices proposed (and proved to be well defined) in parallel in (Chen et al., 2011) and (Pascal et al., 2013), based on Tyler's robust M-estimator (Tyler, 1987) and on…
We derive an optimal shrinkage sample covariance matrix (SCM) estimator which is suitable for high dimensional problems and when sampling from an unspecified elliptically symmetric distribution. Specifically, we derive the optimal (oracle)…
We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…
Many statistical settings call for estimating a population parameter, most typically the population mean, based on a sample of matrices. The most natural estimate of the population mean is the arithmetic mean, but there are many other…
One of the goals in scaling sequential machine learning methods pertains to dealing with high-dimensional data spaces. A key related challenge is that many methods heavily depend on obtaining the inverse covariance matrix of the data. It is…
We tackle covariance estimation in low-sample scenarios, employing a structured covariance matrix with shrinkage methods. These involve convexly combining a low-bias/high-variance empirical estimate with a biased regularization estimator,…
In this paper, we perform a comprehensive study of different covariance and precision matrix estimation methods in the context of minimum variance portfolio allocation. The set of models studied by us can be broadly categorized as: Gaussian…
We propose a distributionally robust formulation for simultaneously estimating the covariance matrix and the precision matrix of a random vector.The proposed model minimizes the worst-case weighted sum of the Frobenius loss of the…
Machine learning models involving discrete latent variables require gradient estimators to facilitate backpropagation in a computationally efficient manner. The most recent addition to the Straight-Through family of estimators, ReinMax, can…
This paper considers the problem of estimating a high-dimensional (HD) covariance matrix when the sample size is smaller, or not much larger, than the dimensionality of the data, which could potentially be very large. We develop a…
A highly popular regularized (shrinkage) covariance matrix estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward the grand mean of the eigenvalues…