Related papers: Estimating principal components of covariance matr…
This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although…
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…
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…
The statistical properties of estimator using covariance matrix for the account of point-to-point correlations due to systematic errors are analyzed. It is shown that the covariance matrix estimator (CME) is consistent for the realistic…
Estimating a covariance matrix is central to high-dimensional data analysis. Empirical analyses of high-dimensional biomedical data, including genomics, proteomics, microbiome, and neuroimaging, among others, consistently reveal strong…
In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a…
Spectrum sensing is a fundamental component is a cognitive radio. In this paper, we propose new sensing methods based on the eigenvalues of the covariance matrix of signals received at the secondary users. In particular, two sensing…
We propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that…
In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal…
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…
This paper is concerned with optimizing the global minimum-variance portfolio's (GMVP) weights in high-dimensional settings where both observation and population dimensions grow at a bounded ratio. Optimizing the GMVP weights is highly…
Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image…
It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…
Networked sensing, where the goal is to perform complex inference using a large number of inexpensive and decentralized sensors, has become an increasingly attractive research topic due to its applications in wireless sensor networks and…
The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in…
Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…
We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to…
Data re-sampling methods such as the delete-one jackknife are a common tool for estimating the covariance of large scale structure probes. In this paper we investigate the concepts of internal covariance estimation in the context of cosmic…
The naive Nystrom extension forms a low-rank approximation to a positive-semidefinite matrix by uniformly randomly sampling from its columns. This paper provides the first relative-error bound on the spectral norm error incurred in this…
We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…