arXiv research

Proofs high-dimensional spectrum convergence of weighted sample covariance.

New method improves covariance estimation for weighted samples.

LoCoV reduces portfolio optimization errors from sample covariance matrices.

Novel approach for SEM in small samples with $p>n$.

This study approximates distances between Gaussian processes and covariance operators using RKHS.

Improved sampling for Diffusion Models by accounting for covariance.

Semi-supervised method boosts two-sample testing with covariate data.

This paper explores how effective sample size, dimensionality, and model performance are related in covariate shift adaptation.

Proposes SVI for covariate-shift generalization with sparse variable independence.

How many samples are sufficient to guarantee that the eigenvectors and eigenvalues of the sample covariance matrix are close to those of the actual covariance matrix? For a wide family of distributions, including distributions with finite second moment and distributions supported in a centered Euclidean ball, we prove …

We study covariance matrix estimation for the case of partially observed random vectors, where different samples contain different subsets of vector coordinates. Each observation is the product of the variable of interest with a $0-1$ Bernoulli random variable. We analyze an unbiased covariance estimator under this mod…

The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of challenges especially when analyzing high-dimensional data sets in which the numb…

ULA estimates covariance of log-concave distributions efficiently.

Robust covariance testing requires significantly more samples in contaminated data.

Estimates covariance matrices with correlations between samples.

In this paper, we provide explicit formulas, in terms of the covariances of sample covariances or sample correlations, for the asymptotic covariances of unrotated factor loading estimates and unique variance estimates. These estimates are extracted from least square, principal, iterative principal component, alpha or i…

The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of 9 improved covariance estimation procedures by using daily returns of 90 highly capitalized US stocks for th…

This paper focuses on the estimation of the sample covariance matrix from low-dimensional random projections of data known as compressive measurements. In particular, we present an unbiased estimator to extract the covariance structure from compressive measurements obtained by a general class of random projection matri…

WeSpeR speeds up non-linear shrinkage for high-dimensional weighted covariance.

Estimates covariance matrices using Markov chain Monte Carlo with improved sample complexity.

DACE estimates covariance from compressed data, improving accuracy.

Proposes a new method to adapt to covariate shifts in supervised learning.

We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for uncorrelated samples. The method allows for exact determination of the experimental spectru…

New methods improve portfolio risk minimization by estimating covariance matrix more accurately.

This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an i.i.d. Gaussian random sample, we establish high dimensional rates of convergence to…

Regularized EM algorithm improves GMM clustering in low sample settings.

Shrunk sample covariance matrix is a factor model of a special form combining some (typically, style) risk factor(s) and principal components with a (block-)diagonal factor covariance matrix. As such, shrinkage, which essentially inherits out-of-sample instabilities of the sample covariance matrix, is not an alternativ…

Study improves treatment effect estimation using unlabeled covariates.

Efficiently estimates prediction error in regression with Gaussian covariates under privacy constraints.

The paper proposes AIS for Bayesian inversion of multioutput signals with covariance estimation.

Optimizes sample reweighting to match laws under covariate shift using Wasserstein distance.

Study on estimating distances between covariance operators and Gaussian processes.

We propose a novel estimation approach for the covariance matrix based on the $l_1$-regularized approximate factor model. Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes the pervasiveness assumption generally adopted for the standard approximate factor…

Simple private estimators for mean and covariance outperform existing methods.

Robustly estimates linear regression coefficients with adversarial and noisy data.

Regularized EM algorithm improves clustering performance with small sample sizes.

The covariance matrix of a $p$-dimensional random variable is a fundamental quantity in data analysis. Given $n$ i.i.d. observations, it is typically estimated by the sample covariance matrix, at a computational cost of $O(np^{2})$ operations. When $n,p$ are large, this computation may be prohibitively slow. Moreover, …

The paper examines extreme value statistics of high-dimensional sample covariances, with applications in finance and image analysis.

The paper defines conditions for Gaussian process sample path regularity.

New algorithm reduces sample complexity for sparse linear regression.

Study precise sample covariance error for Gaussian centered data.

Study extends bounds on sample covariance matrices with general dependence.

Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest eigenvalue of the sample covariance matrix over a sliding window to detect the change. T…

A new LDA model with covariates for mixed-membership clusters.

Study improves covariance estimation for SGD under Markovian data, matching best rates.

Better signal detection in undersampled data using joint and cross covariances.

Paper develops an online covariance estimator for nonsmooth stochastic approximation problems.

EiGLasso speeds up sparse Kronecker-sum covariance estimation.