Related papers: Matrix Completion under Low-Rank Missing Mechanism

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…

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…

We propose a theory for matrix completion that goes beyond the low-rank structure commonly considered in the literature and applies to general matrices of low description complexity. Specifically, complexity of the sets of matrices…

Missing values challenge data analysis because many supervised and unsupervised learning methods cannot be applied directly to incomplete data. Matrix completion based on low-rank assumptions are very powerful solution for dealing with…

In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into submatrices which are filled with a proposed trimming step and then are recombined to form a low-rank…

We study the completion of approximately low rank matrices with entries missing not at random (MNAR). In the context of typical large-dimensional statistical settings, we establish a framework for the performance analysis of the nuclear…

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…

This paper considers the low-observability state estimation problem in power distribution networks and develops a decentralized state estimation algorithm leveraging the matrix completion methodology. Matrix completion has been shown to be…

In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…

We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…

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,…

Modern surveys with large sample sizes and growing mixed-type questionnaires require robust and scalable analysis methods. In this work, we consider recovering a mixed dataframe matrix, obtained by complex survey sampling, with entries…

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

For many machine learning tasks, the input data lie on a low-dimensional manifold embedded in a high dimensional space and, because of this high-dimensional structure, most algorithms are inefficient. The typical solution is to reduce the…

Low-rank matrix completion is an important problem with extensive real-world applications. When observations are uniformly sampled from the underlying matrix entries, existing methods all require the matrix to be incoherent. This paper…

A well-known method for completing low-rank matrices based on convex optimization has been established by Cand{\`e}s and Recht. Although theoretically complete, the method may not entirely solve the low-rank matrix completion problem. This…

Low-rank matrix approximation is one of the central concepts in machine learning, with applications in dimension reduction, de-noising, multivariate statistical methodology, and many more. A recent extension to LRMA is called low-rank…

The low-rank matrix completion problem asks whether a given real matrix with missing values can be completed so that the resulting matrix has low rank or is close to a low-rank matrix. The completed matrix is often required to satisfy…

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…

The problem of completing high-dimensional matrices from a limited set of observations arises in many big data applications, especially, recommender systems. Existing matrix completion models generally follow either a memory- or a…