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

The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out…

The aim of reduced rank regression is to connect multiple response variables to multiple predictors. This model is very popular, especially in biostatistics where multiple measurements on individuals can be re-used to predict multiple…

In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction…

The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…

Recommender systems can be formulated as a matrix completion problem, predicting ratings from user and item parameter vectors. Optimizing these parameters by subsampling data becomes difficult as the number of users and items grows. We…

We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica…

The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…

We present novel algorithmic techniques to efficiently verify the Kruskal rank of matrices that arise in sparse linear regression, tensor decomposition, and latent variable models. Our unified framework combines randomized hashing…

We consider the problem of automatic variable selection in a linear model with asymmetric or heavy-tailed errors when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least…

We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…

Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…

Rank aggregation systems collect ordinal preferences from individuals to produce a global ranking that represents the social preference. Rank-breaking is a common practice to reduce the computational complexity of learning the global…

Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training…

We are interested in the estimation of a rank-one tensor signal when only a portion $\varepsilon$ of its noisy observation is available. We show that the study of this problem can be reduced to that of a random matrix model whose spectral…

This paper presents a unified rank-based inferential procedure for fitting the accelerated failure time model to partially interval-censored data. A Gehan-type monotone estimating function is constructed based on the idea of the familiar…

We consider penalized regression models under a unified framework where the particular method is determined by the form of the penalty term. We propose a fully Bayesian approach that incorporates both sparse and dense settings and show how…

Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…

This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results…

Given data sampled from a number of variables, one is often interested in the underlying causal relationships in the form of a directed acyclic graph. In the general case, without interventions on some of the variables it is only possible…