Related papers: Matrix Completion with Heterogonous Cost
Matrix completion is a ubiquitous tool in machine learning and data analysis. Most work in this area has focused on the number of observations necessary to obtain an accurate low-rank approximation. In practice, however, the cost of…
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…
In this paper, we consider matrix completion from non-uniformly sampled entries including fully observed and partially observed columns. Specifically, we assume that a small number of columns are randomly selected and fully observed, and…
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 study the problem of exact completion for $m \times n$ sized matrix of rank $r$ with the adaptive sampling method. We introduce a relation of the exact completion problem with the sparsest vector of column and row spaces (which we call…
This paper studies the open problem of conformalized entry prediction in a row/column-exchangeable matrix. The matrix setting presents novel and unique challenges, but there exists little work on this interesting topic. We meticulously…
This paper is motivated by the fact that many systems need to be maintained continually while the underlying costs change over time. The challenge is to continually maintain near-optimal solutions to the underlying optimization problems,…
Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…
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…
In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…
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…
The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…
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…
This paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces. This generalizes the standard low-rank matrix completion…
We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: under what condition there will be (at least locally) unique solution to the matrix completion…
We consider two matrix completion problems, in which we are given a matrix with missing entries and the task is to complete the matrix in a way that (1) minimizes the rank, or (2) minimizes the number of distinct rows. We study the…
Matrix completion tackles the task of predicting missing values in a low-rank matrix based on a sparse set of observed entries. It is often assumed that the observation pattern is generated uniformly at random or has a very specific…
Matrix completion problem has been investigated under many different conditions since Netflix announced the Netflix Prize problem. Many research work has been done in the field once it has been discovered that many real life dataset could…
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…
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…