Related papers: Leveraging Shared Factor Structures for Enhanced M…

In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…

Trace norm regularization is a widely used approach for learning low rank matrices. A standard optimization strategy is based on formulating the problem as one of low rank matrix factorization which, however, leads to a non-convex problem.…

The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification…

Supervised learning methods with missing data have been extensively studied not just due to the techniques related to low-rank matrix completion. Also in unsupervised learning one often relies on imputation methods. As a matter of fact,…

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…

Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…

We consider minimization problems with structured objective function and smooth constraints, and present a flexible framework that combines the beneficial regularization effects of (exact) penalty and interior-point methods. In the fully…

Motivated by an application in computational biology, we consider low-rank matrix factorization with $\{0,1\}$-constraints on one of the factors and optionally convex constraints on the second one. In addition to the non-convexity shared…

Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…

The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically…

Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…

The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…

Matrix factorization models have been extensively studied as a valuable test-bed for understanding the implicit biases of overparameterized models. Although both low nuclear norm and low rank regularization have been studied for these…

Modern matrix completion problems often involve heterogeneous data whose rows simultaneously belong to many meta-categories, such as demographic and age groups in recommendation systems, or region and recording session labels in neural…

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…

The paper deals with the problem of penalized empirical risk minimization over a convex set of linear functionals on the space of Hermitian matrices with convex loss and nuclear norm penalty. Such penalization is often used in low rank…

In this paper we consider a general matrix factorization model which covers a large class of existing models with many applications in areas such as machine learning and imaging sciences. To solve this possibly nonconvex, nonsmooth and…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

In this paper, nonconvex and nonsmooth models for compressed sensing (CS) and low rank matrix completion (MC) is studied. The problem is formulated as a nonconvex regularized leat square optimization problems, in which the l0-norm and the…

Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…