Related papers: Adaptive Multinomial Matrix Completion
We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of…
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…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…
The need to predict or fill-in missing data, often referred to as matrix completion, is a common challenge in today's data-driven world. Previous strategies typically assume that no structural difference between observed and missing entries…
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,…
We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…
We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…
We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover…
Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…
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…
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…
Recently theoretical guarantees have been obtained for matrix completion in the non-uniform sampling regime. In particular, if the sampling distribution aligns with the underlying matrix's leverage scores, then with high probability nuclear…
An incoherent low-rank matrix can be efficiently reconstructed after observing a few of its entries at random, and then solving a convex program that minimizes the nuclear norm. In many applications, in addition to these entries,…
Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict…
Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns. We consider the problem of estimating…
This paper considers the problem of completing a rating matrix based on sub-sampled matrix entries as well as observed social graphs and hypergraphs. We show that there exists a \emph{sharp threshold} on the sample probability for the task…
Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…
Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…
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…