Related papers: Matrix completion with data-dependent missingness …

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…

This paper considers the problem of estimating a low-rank matrix from the observation of all or a subset of its entries in the presence of Poisson noise. When we observe all entries, this is a problem of matrix denoising; when we observe…

Many results have been proved for various nuclear norm penalized estimators of the uniform sampling matrix completion problem. However, most of these estimators are not robust: in most of the cases the quadratic loss function and its…

Matrix completion is a classical problem that has received recurring interest across a wide range of fields. In this paper, we revisit this problem in an ultra-sparse sampling regime, where each entry of an unknown, $n\times d$ matrix $M$…

This paper studies decision-making and statistical inference for two-sided matching markets via matrix completion. In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise…

This paper proposes an imputation procedure that uses the factors estimated from a tall block along with the re-rotated loadings estimated from a wide block to impute missing values in a panel of data. Assuming that a strong factor…

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…

Many datasets suffer from missing values due to various reasons,which not only increases the processing difficulty of related tasks but also reduces the accuracy of classification. To address this problem, the mainstream approach is to use…

Matching markets face increasing needs to learn the matching qualities between demand and supply for effective design of matching policies. In practice, the matching rewards are high-dimensional due to the growing diversity of participants.…

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…

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.…

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…

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…

Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in control theory, machine learning, and discrete geometry. This class of optimization problems, known as rank minimization, is…

The matrix recovery (completion) problem, a central problem in data science and theoretical computer science, is to recover a matrix $A$ from a relatively small sample of entries. While such a task is impossible in general, it has been…

For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…

Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the…

Recovering a low rank matrix from a subset of its entries, some of which may be corrupted, is known as the robust matrix completion (RMC) problem. Existing RMC methods have several limitations: they require a relatively large number of…

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…

Matrix completion is widely used in machine learning, engineering control, image processing, and recommendation systems. Currently, a popular algorithm for matrix completion is Singular Value Threshold (SVT). In this algorithm, the singular…