Related papers: Nonconvex Rectangular Matrix Completion via Gradie…

The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…

In this paper we study the problem of recovering a low-rank matrix from a number of random linear measurements that are corrupted by outliers taking arbitrary values. We consider a nonsmooth nonconvex formulation of the problem, in which we…

Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and…

We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs…

We formulate the problem of matrix completion with and without side information as a non-convex optimization problem. We design fastImpute based on non-convex gradient descent and show it converges to a global minimum that is guaranteed to…

In this paper, we analyze the mirror descent algorithm for non-smooth optimization problems in which the objective function is relatively strongly convex, without relying on the standard Lipschitz continuity assumption commonly used in the…

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…

Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…

Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…

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 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…

In this paper, we study the gradient descent-ascent method for convex-concave saddle-point problems. We derive a new non-asymptotic global convergence rate in terms of distance to the solution set by using the semidefinite programming…

This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle…

Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…

In this paper, we study the popularly dubbed matrix completion problem, where the task is to "fill in" the unobserved entries of a matrix from a small subset of observed entries, under the assumption that the underlying matrix is of…

The goal of a recommendation system is to predict the interest of a user in a given item by exploiting the existing set of ratings as well as certain user/item features. A standard approach to modeling this problem is Inductive Matrix…

While there has been a significant amount of work studying gradient descent techniques for non-convex optimization problems over the last few years, all existing results establish either local convergence with good rates or global…

This paper studies an optimization problem on the sum of traces of matrix quadratic forms in $m$ semi-orthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, the…

We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…

This paper investigates distributed zeroth-order optimization for smooth nonconvex problems, targeting the trade-off between convergence rate and sampling cost per zeroth-order gradient estimation in current algorithms that use either the…