Related papers: Matrix Completion for the Independence Model

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 paper we study methods for estimating causal effects in settings with panel data, where some units are exposed to a treatment during some periods and the goal is estimating counterfactual (untreated) outcomes for the treated…

We study the problem of testing whether the missing values of a potentially high-dimensional dataset are Missing Completely at Random (MCAR). We relax the problem of testing MCAR to the problem of testing the compatibility of a collection…

This article investigates the problem of noisy low-rank matrix completion with a shared factor structure, leveraging the auxiliary information from the missing indicator matrix to enhance prediction accuracy. Despite decades of development…

In this article, we introduce the concept of the column-sufficient W-property for a set of matrices and prove the convexity of the solution set for the Extended Horizontal Linear Complementarity Problem. Additionally, we present an…

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…

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…

We revisit the class of column competent matrices and study some matrix theoretic properties of this class. The local $w$-uniqueness of the solutions to the linear complementarity problem can be identified by the column competent matrices.…

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…

Alongside consistency, completeness of information is one of the key factors influencing data quality. The objective of this paper is to define ways of treating missing entries in pairwise comparisons (PC) method with respect to…

This paper studies the problem of deterministic rank-one matrix completion. It is known that the simplest semidefinite programming relaxation, involving minimization of the nuclear norm, does not in general return the solution for this…

Completion problems, of recovering a point from a set of observed coordinates, are abundant in applications to image reconstruction, phylogenetics, and data science. We consider a completion problem coming from algebraic statistics: to…

We study alternating minimization for matrix completion in the simplest possible setting: completing a rank-one matrix from a revealed subset of the entries. We bound the asymptotic convergence rate by the variational characterization of…

Pairwise comparison matrices often exhibit inconsistency, therefore many indices have been suggested to measure their deviation from a consistent matrix. A set of axioms has been proposed recently that is required to be satisfied by any…

We describe a way to complete a correlation matrix that is not fully specified. Such matrices often arise in financial applications when the number of stochastic variables becomes large or when several smaller models are combined in a…

We consider the problem of low canonical polyadic (CP) rank tensor completion. A completion is a tensor whose entries agree with the observed entries and its rank matches the given CP rank. We analyze the manifold structure corresponding to…

Techniques of matrix completion aim to impute a large portion of missing entries in a data matrix through a small portion of observed ones. In practice including collaborative filtering, prior information and special structures are usually…

Low-rank matrix completion has been studied extensively under various type of categories. The problem could be categorized as noisy completion or exact completion, also active or passive completion algorithms. In this paper we focus on…

In this letter, we study the deterministic sampling patterns for the completion of low rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling…

A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent…