Related papers: Random Matrix Derived Shrinkage of Spectral Precis…
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…
Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t-distributed measurement noise are proposed. The algorithms use a variational Bayes based posterior approximation with coupled location and skewness…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original…
Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This…
We propose an l1-regularized likelihood method for estimating the inverse covariance matrix in the high-dimensional multivariate normal model in presence of missing data. Our method is based on the assumption that the data are missing at…
The main theme of this paper is a modification of the likelihood ratio test (LRT) for testing high dimensional covariance matrix. Recently, the correct asymptotic distribution of the LRT for a large-dimensional case (the case $p/n$…
We introduce a dynamic mechanism for the solution of analytically-tractable substructure in probabilistic programs, using conjugate priors and affine transformations to reduce variance in Monte Carlo estimators. For inference with…
Estimating the number of signals embedded in noise is a fundamental problem in array signal processing. The classic RMT estimator based on random matrix theory (RMT) tends to under-estimate the number of signals as it does not consider the…
In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that…
In the first part of this work, we develop a novel scheme for solving nonparametric regression problems. That is the approximation of possibly low regular and noised functions from the knowledge of their approximate values given at some…
In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…
This paper develops a novel approach to random effects estimation and individual-level forecasting in micropanels, targeting individual accuracy rather than aggregate performance. The conventional shrinkage methods used in the literature,…
Randomized matrix algorithms have become workhorse tools in scientific computing and machine learning. To use these algorithms safely in applications, they should be coupled with posterior error estimates to assess the quality of the…
This chapter reviews methods for linear shrinkage of the sample covariance matrix (SCM) and matrices (SCM-s) under elliptical distributions in single and multiple populations settings, respectively. In the single sample setting a popular…
Gradient estimation in models with discrete latent variables is a challenging problem, because the simplest unbiased estimators tend to have high variance. To counteract this, modern estimators either introduce bias, rely on multiple…
Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…
This paper considers the regularized estimation of covariance matrices (CM) of high-dimensional (compound) Gaussian data for minimum variance distortionless response (MVDR) beamforming. Linear shrinkage is applied to improve the accuracy…
We develop a class of data-adaptive shrinkage estimators for high-dimensional covariance estimation in which the shrinkage target is a Reynolds projection of the sample covariance under a finite symmetry group selected from a candidate…
We address the problem of robust sparse estimation of the precision matrix for heavy-tailed distributions in high-dimensional settings. In such high-dimensional contexts, we observe that the covariance matrix can be approximated by a…