Related papers: Matrix Completion via Residual Spectral Matching

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for…

We recently showed in [1] the superiority of certain structured coding matrices ensembles (such as partial row-orthogonal) for sparse superposition codes when compared with purely random matrices with i.i.d. entries, both…

The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the…

This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…

In this paper, we propose two new algorithms for transduction with Matrix Completion (MC) problem. The joint MC and prediction tasks are addressed simultaneously to enhance the accuracy, i.e., the label matrix is concatenated to the data…

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…

Most of the existing works on provable guarantees for low-rank matrix completion algorithms rely on some unrealistic assumptions such that matrix entries are sampled randomly or the sampling pattern has a specific structure. In this work,…

In this paper, we propose an algorithm referred to as multipath matching pursuit that investigates multiple promising candidates to recover sparse signals from compressed measurements. Our method is inspired by the fact that the problem to…

We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when…

In this work, we develop a new complexity metric for an important class of low-rank matrix optimization problems in both symmetric and asymmetric cases, where the metric aims to quantify the complexity of the nonconvex optimization…

Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and…

Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for…

This paper deals with the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We propose a new nuclear norm penalized estimator of $A_0$ and…

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…

Sparse linear regression methods including the well-known LASSO and the Dantzig selector have become ubiquitous in the engineering practice, including in medical imaging. Among other tasks, they have been successfully applied for the…

We consider the problem of finding a low rank symmetric matrix satisfying a system of linear equations, as appears in phase retrieval. In particular, we solve the gauge dual formulation, but use a fast approximation of the spectral…

Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially…

This paper is concerned with noisy matrix completion--the problem of recovering a low-rank matrix from partial and noisy entries. Under uniform sampling and incoherence assumptions, we prove that a tuning-free square-root matrix completion…

This paper presents novel algorithms which exploit the intrinsic algebraic and combinatorial structure of the matrix completion task for estimating missing en- tries in the general low rank setting. For positive data, we achieve results…

Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…