Related papers: Matrix Completion with Sparse Noisy Rows
We consider the problem of recovering an unknown effectively $(s_1,s_2)$-sparse low-rank-$R$ matrix $X$ with possibly non-orthogonal rank-$1$ decomposition from incomplete and inaccurate linear measurements of the form $y = \mathcal A (X) +…
This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our…
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…
The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
We extend the theory of low-rank matrix recovery and completion to the case when Poisson observations for a linear combination or a subset of the entries of a matrix are available, which arises in various applications with count data. We…
We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…
Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as…
This paper studies the stability of low-rank implicit regularization in perturbed deep matrix factorization, where the target matrix is corrupted by a noise matrix. We first derive sufficient spectral conditions under which gradient descent…
Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this…
We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…
Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
We consider the problem of reconstructing a low rank matrix from noisy observations of a subset of its entries. This task has applications in statistical learning, computer vision, and signal processing. In these contexts, "noise"…
We consider the matrix completion problem of recovering a structured matrix from noisy and partial measurements. Recent works have proposed tractable estimators with strong statistical guarantees for the case where the underlying matrix is…
In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison…