Related papers: Low-Rank Approximations of Nonseparable Panel Mode…

Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…

This article is an extended version of previous work of the authors [40, 41] on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic…

We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among…

This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified.…

Hierarchical panel data models have recently garnered significant attention. This study contributes to the relevant literature by introducing a novel three-dimensional (3D) hierarchical panel data model, which integrates panel regression…

Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…

This paper makes a selective survey on the recent development of the factor model and its application on statistical learnings. We focus on the perspective of the low-rank structure of factor models, and particularly draws attentions to…

We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…

In this paper, a statistical model for panel data with unobservable grouped factor structures which are correlated with the regressors and the group membership can be unknown. The factor loadings are assumed to be in different subspaces and…

Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…

We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…

Missing Not At Random (MNAR) values lead to significant biases in the data, since the probability of missingness depends on the unobserved values.They are ''not ignorable'' in the sense that they often require defining a model for the…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…

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…

By removing irrelevant and redundant features, feature selection aims to find a good representation of the original features. With the prevalence of unlabeled data, unsupervised feature selection has been proven effective in alleviating the…