Related papers: Covariance Matrix Estimation from Correlated Sub-G…

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix…

Data analysis in cosmology requires reliable covariance matrices. Covariance matrices derived from numerical simulations often require a very large number of realizations to be accurate. When a theoretical model for the covariance matrix…

This paper considers regularizing a covariance matrix of $p$ variables estimated from $n$ observations, by hard thresholding. We show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is…

Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…

This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A major focus is on the derivation of a rate sharp minimax…

Estimating covariance matrices is a problem of fundamental importance in multivariate statistics. In practice it is increasingly frequent to work with data matrices $X$ of dimension $n\times p$, where $p$ and $n$ are both large. Results…

This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis…

We investigate the bias and error in estimates of the cosmological parameter covariance matrix, due to sampling or modelling the data covariance matrix, for likelihood width and peak scatter estimators. We show that these estimators do not…

Minimax detection of Gaussian stochastic sequences (signals) with unknown covariance matrices is studied. For a fixed false alarm probability (1-st kind error probability), the performance of the minimax detection is being characterized by…

Gaussian graphical models are widely used to represent correlations among entities but remain vulnerable to data corruption. In this work, we introduce a modified trimmed-inner-product algorithm to robustly estimate the covariance in an…

Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…

We establish a large deviation principle for the empirical spectral measure of a sample covariance matrix with sub-Gaussian entries, which extends Bordenave and Caputo's result for Wigner matrices having the same type of entries [7]. To…

We study sample covariance matrices arising from rectangular random matrices with i.i.d. columns. It was previously known that the resolvent of these matrices admits a deterministic equivalent when the spectral parameter stays bounded away…

We study the estimation error of constrained M-estimators, and derive explicit upper bounds on the expected estimation error determined by the Gaussian width of the constraint set. Both of the cases where the true parameter is on the…

Model uncertainty quantification is an essential component of effective data assimilation. Model errors associated with sub-grid scale processes are often represented through stochastic parameterizations of the unresolved process. Many…

We study the covariance of the cross-power spectrum of different tracers for the large-scale structure. We develop the counts-in-cells framework for the multi-tracer approach, and use this to derive expressions for the full non-Gaussian…

We present simple differentially private estimators for the mean and covariance of multivariate sub-Gaussian data that are accurate at small sample sizes. We demonstrate the effectiveness of our algorithms both theoretically and empirically…

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…

The problem of estimating the covariance matrix $\Sigma$ of a $p$-variate distribution based on its $n$ observations arises in many data analysis contexts. While for $n>p$, the classical sample covariance matrix $\hat{\Sigma}_n$ is a good…

Monte Carlo matrix trace estimation is a popular randomized technique to estimate the trace of implicitly-defined matrices via averaging quadratic forms across several observations of a random vector. The most common approach to analyze the…