Related papers: Matrix Completion over Finite Fields: Bounds and B…
Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…
A new algorithm, termed subspace evolution and transfer (SET), is proposed for solving the consistent matrix completion problem. In this setting, one is given a subset of the entries of a low-rank matrix, and asked to find one low-rank…
We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation…
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…
On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…
The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and…
The problem of low-rank matrix completion has recently generated a lot of interest leading to several results that offer exact solutions to the problem. However, in order to do so, these methods make assumptions that can be quite…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…
The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to…
This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…
We consider the problem of noisy 1-bit matrix completion under an exact rank constraint on the true underlying matrix $M^*$. Instead of observing a subset of the noisy continuous-valued entries of a matrix $M^*$, we observe a subset of…
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…
We investigate the problem of completing partial matrices to rank-one matrices in the standard simplex. The motivation for studying this problem comes from statistics: A lack of eligible completion can provide a falsification test for…
Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…
The problem of completing a large matrix with lots of missing entries has received widespread attention in the last couple of decades. Two popular approaches to the matrix completion problem are based on singular value thresholding and…
This paper proposes a new method for solving the well-known rank aggregation problem from pairwise comparisons using the method of low-rank matrix completion. The partial and noisy data of pairwise comparisons is transformed into a matrix…
We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper…
We solve the Matrix Completion (MC) problem based on manifold optimization by incorporating the side information under which the columns of the intended matrix are drawn from a union of low dimensional subspaces. It is proved that this side…
Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as…
We present a novel algorithm for the completion of low-rank matrices whose entries are limited to a finite discrete alphabet. The proposed method is based on the recently-emerged proximal gradient (PG) framework of optimization theory,…