相关论文: Matrix Completion from Noisy Entries

Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies…

Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well…

A general framework based on Gaussian models and a MAP-EM algorithm is introduced in this paper for solving matrix/table completion problems. The numerical experiments with the standard and challenging movie ratings data show that the…

This paper describes a fast algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex…

Motivated by the increasing demand for multi-source data integration in various scientific fields, in this paper we study matrix completion in scenarios where the data exhibits certain block-wise missing structures -- specifically, where…

We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…

In this paper we study the problem of reconstruction of a low-rank matrix observed with additive Gaussian noise. First we show that under mild assumptions (about the prior distribution of the signal matrix) we can restrict our attention to…

A matrix network is a family of matrices, with relatedness modeled by a weighted graph. We consider the task of completing a partially observed matrix network. We assume a novel sampling scheme where a fraction of matrices might be…

We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…

Low rank matrix recovery problems, including matrix completion and matrix sensing, appear in a broad range of applications. In this work we present GNMR -- an extremely simple iterative algorithm for low rank matrix recovery, based on a…

Completing a data matrix X has become an ubiquitous problem in modern data science, with applications in recommender systems, computer vision, and networks inference, to name a few. One typical assumption is that X is low-rank. A more…

A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…

We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a…

In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…

The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…

This paper addresses the large-scale acquisition of end-to-end network performance. We made two distinct contributions: ordinal rating of network performance and inference by matrix completion. The former reduces measurement costs and…

In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…

Previous work regarding low-rank matrix recovery has concentrated on the scenarios in which the matrix is noise-free and the measurements are corrupted by noise. However, in practical application, the matrix itself is usually perturbed by…

We consider the related tasks of matrix completion and matrix approximation from missing data and propose adaptive sampling procedures for both problems. We show that adaptive sampling allows one to eliminate standard incoherence…

We present a method for the reconstruction of networks, based on the order of nodes visited by a stochastic branching process. Our algorithm reconstructs a network of minimal size that ensures consistency with the data. Crucially, we show…