Related papers: Rank penalized estimators for high-dimensional mat…

We observe $(X_i,Y_i)_{i=1}^n$ where the $Y_i$'s are real valued outputs and the $X_i$'s are $m\times T$ matrices. We observe a new entry $X$ and we want to predict the output $Y$ associated with it. We focus on the high-dimensional…

We consider the high-dimensional inference problem where the signal is a low-rank matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension…

We consider in this paper the problem of estimating a parameter matrix from observations which are affected by two types of noise components: (i) a sparse noise sequence which, whenever nonzero can have arbitrarily large amplitude (ii) and…

We present a unified framework for low-rank matrix estimation with nonconvex penalties. We first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty.…

The matrix completion problem consists in reconstructing a matrix from a sample of entries, possibly observed with noise. A popular class of estimator, known as nuclear norm penalized estimators, are based on minimizing the sum of a data…

This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…

We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…

Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional…

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 consider the problem of recovering an unknown low-rank matrix X with (possibly) non-orthogonal, effectively sparse rank-1 decomposition from measurements y gathered in a linear measurement process A. We propose a variational formulation…

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 examine the problem of estimating the trace of a matrix $A$ when given access to an oracle which computes $x^\dagger A x$ for an input vector $x$. We make use of the basis vectors from a set of mutually unbiased bases, widely studied in…

We consider the framework of penalized estimation where the penalty term is given by a real-valued polyhedral gauge, which encompasses methods such as LASSO, generalized LASSO, SLOPE, OSCAR, PACS and others. Each of these estimators is…

Modern data analysis depends increasingly on estimating models via flexible high-dimensional or nonparametric machine learning methods, where the identification of structural parameters is often challenging and untestable. In linear…

This paper introduces a novel framework for estimation and inference in penalized M-estimators applied to robust high-dimensional linear regression models. Traditional methods for high-dimensional statistical inference, which predominantly…

Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…

We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and…

Low-rank matrix completion has been studied extensively under various type of categories. The problem could be categorized as noisy completion or exact completion, also active or passive completion algorithms. In this paper we focus on…

High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…

We introduce mixed model trace regression (MMTR), a mixed model linear regression extension for scalar responses and high-dimensional matrix-valued covariates. MMTR's fixed effects component is equivalent to trace regression, with an…