Related papers: Estimation of functionals of sparse covariance mat…

We characterize the first-order sensitivity of approximately recovering a low-rank matrix from linear measurements, a standard problem in compressed sensing. A special case covered by our analysis is approximating an incomplete matrix by a…

The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…

We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric…

In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…

Our main interest is the low-rank approximation of a matrix in R^m.n under a weighted Frobenius norm. This norm associates a weight to each of the (m x n) matrix entries. We conjecture that the number of approximations is at most min(m, n).…

In functional data analysis, functional linear regression has attracted significant attention recently. Herein, we consider the case where both the response and covariates are functions. There are two available approaches for addressing…

We study nonasymptotic minimax estimation of the linear functional $L(\theta)=\eta^\top \theta$ for a high-dimensional $s$-sparse mean vector with an arbitrary loading vector $\eta$. For symmetric noise with exponentially decaying tails, we…

The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered…

We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…

Using the $\ell_1$-norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account…

We study the minimax estimation of covariance eigenfunctions and eigenvalues in functional principal component analysis when $n$ trajectories are observed at $p$ common grid points with additive noise. We consider covariance kernels with…

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…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…

We consider the related problems of estimating the $l_2$-norm and the squared $l_2$-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that the regression parameter is null under sparse…

This paper concerns the problem of matrix completion, which is to estimate a matrix from observations in a small subset of indices. We propose a calibrated spectrum elastic net method with a sum of the nuclear and Frobenius penalties and…

We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we…

We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and…

Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental problem in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Towards bridging…

Given a dictionary of $M_n$ initial estimates of the unknown true regression function, we aim to construct linearly aggregated estimators that target the best performance among all the linear combinations under a sparse $q$-norm ($0 \leq q…

Functional data analysis has been extensively conducted. In this study, we consider a partially functional model, under which some covariates are scalars and have linear effects, while some other variables are functional and have…