Related papers: A Structure-Tensor Approach to Integer Matrix Comp…
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…
Despite the popularity of low-rank matrix completion, the majority of its theory has been developed under the assumption of random observation patterns, whereas very little is known about the practically relevant case of non-random…
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…
We give the first algorithm for Matrix Completion whose running time and sample complexity is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix.…
We consider the statistical inference for noisy incomplete binary (or 1-bit) matrix. Despite the importance of uncertainty quantification to matrix completion, most of the categorical matrix completion literature focuses on point estimation…
We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…
This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems and is a generalization…
Does a given system of linear equations with nonnegative constraints have an integer solution? This is a fundamental question in many areas. In statistics this problem arises in data security problems for contingency table data and also is…
We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for…
Regular medical records are useful for medical practitioners to analyze and monitor patient health status especially for those with chronic disease, but such records are usually incomplete due to unpunctuality and absence of patients. In…
In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware…
Tensor ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally…
In some significant applications such as data forecasting, the locations of missing entries cannot obey any non-degenerate distributions, questioning the validity of the prevalent assumption that the missing data is randomly chosen…
This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…
This is a survey of the recent progress and open questions on the structure of the sets of 0-1 and non-negative integer matrices with prescribed row and column sums. We discuss cardinality estimates, the structure of a random matrix from…
To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span…
We consider the problem of tensor completion with graphs serving as side information to represent interrelationships among variables. Existing approaches suffer from several limitations: (1) they are often task-specific and lack generality…
Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we…