Related papers: Optimal Linear Shrinkage Estimator for Large Dimen…

In this paper, we present several estimators of the diagonal elements of the inverse of the covariance matrix, called precision matrix, of a sample of iid random vectors. The focus is on high dimensional vectors having a sparse precision…

It is well-known that, in Gaussian two-group separation, the optimally discriminating projection direction can be estimated without any knowledge on the group labels. In this work, we \revision{gather} several such unsupervised estimators…

We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…

One of the goals in scaling sequential machine learning methods pertains to dealing with high-dimensional data spaces. A key related challenge is that many methods heavily depend on obtaining the inverse covariance matrix of the data. It is…

In a linear regression model with random design, we consider a family of candidate models from which we want to select a `good' model for prediction out-of-sample. We fit the models using block shrinkage estimators, and we focus on the…

Analyzing large samples of high-dimensional data under dependence is a challenging statistical problem as long time series may have change points, most importantly in the mean and the marginal covariances, for which one needs valid tests.…

Last decade witnesses significant methodological and theoretical advances in estimating large precision matrices. In particular, there are scientific applications such as longitudinal data, meteorology and spectroscopy in which the ordering…

In optimal covariance cleaning theory, minimizing the Frobenius norm between the true population covariance matrix and a rotational invariant estimator is a key step. This estimator can be obtained asymptotically for large covariance…

A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…

We establish large sample approximations for an arbitray number of bilinear forms of the sample variance-covariance matrix of a high-dimensional vector time series using $ \ell_1$-bounded and small $\ell_2$-bounded weighting vectors.…

Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a…

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…

To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling…

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation $\mathfrak{X}$ of the sum of an approximately) low…

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum…

Unlike the ordinary least-squares (OLS) estimator for the linear model, a ridge regression linear model provides coefficient estimates via shrinkage, usually with improved mean-square and prediction error. This is true especially when the…

This work addresses the issue of large covariance matrix estimation in high-dimensional statistical analysis. Recently, improved iterative algorithms with positive-definite guarantee have been developed. However, these algorithms cannot be…

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…

We give a new algorithm for the estimation of the cross-covariance matrix $\mathbb{E} XY'$ of two large dimensional signals $X\in\mathbb{R}^n$, $Y\in \mathbb{R}^p$ in the context where the number $T$ of observations of the pair $(X,Y)$ is…

Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…