Related papers: High-dimensional covariance matrix estimation with…
The problem of estimating a normal covariance matrix is considered from a decision-theoretic point of view, where the dimension of the covariance matrix is larger than the sample size. This paper addresses not only the nonsingular case but…
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…
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…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…
The estimation of high dimensional precision matrices has been a central topic in statistical learning. However, as the number of parameters scales quadratically with the dimension $p$, many state-of-the-art methods do not scale well to…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
In many astrophysical settings covariance matrices of large datasets have to be determined empirically from a finite number of mock realisations. The resulting noise degrades inference and precludes it completely if there are fewer…
We first study the properties of solutions of quadratic programs with linear equality constraints whose parameters are estimated from data in the high-dimensional setting where p, the number of variables in the problem, is of the same order…
A sample covariance matrix $\boldsymbol{S}$ of completely observed data is the key statistic in a large variety of multivariate statistical procedures, such as structured covariance/precision matrix estimation, principal component analysis,…
Multiview latent-variable models provide a fundamental framework for discrete data analysis, with applications to latent structure models, topic models, and mixtures of product distributions. In the discrete setting, the joint distribution…
We consider high dimensional $M$-estimation in settings where the response $Y$ is possibly missing at random and the covariates $\mathbf{X} \in \mathbb{R}^p$ can be high dimensional compared to the sample size $n$. The parameter of interest…
We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…
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…
This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
Fitting high-dimensional data involves a delicate tradeoff between faithful representation and the use of sparse models. Too often, sparsity assumptions on the fitted model are too restrictive to provide a faithful representation of the…