Related papers: Matrix Completion in Almost-Verification Time
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…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…
Weighted low rank approximation is a fundamental problem in numerical linear algebra, and it has many applications in machine learning. Given a matrix $M \in \mathbb{R}^{n \times n}$, a non-negative weight matrix $W \in \mathbb{R}_{\geq…
We address the rectangular matrix completion problem by lifting the unknown matrix to a positive semidefinite matrix in higher dimension, and optimizing a nonconvex objective over the semidefinite factor using a simple gradient descent…
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…
The existing matrix completion methods focus on optimizing the relaxation of rank function such as nuclear norm, Schatten-p norm, etc. They usually need many iterations to converge. Moreover, only the low-rank property of matrices is…
We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
Leverage scores, loosely speaking, reflect the importance of the rows and columns of a matrix. Ideally, given the leverage scores of a rank-$r$ matrix $M\in\mathbb{R}^{n\times n}$, that matrix can be reliably completed from just…
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…
The low-rank matrix approximation problem with respect to the entry-wise $\ell_{\infty}$-norm is the following: given a matrix $M$ and a factorization rank $r$, find a matrix $X$ whose rank is at most $r$ and that minimizes $\max_{i,j}…
Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…
After the phenomenal success of the PageRank algorithm, many researchers have extended the PageRank approach to ranking graphs with richer structures beside the simple linkage structure. In some scenarios we have to deal with…
The task of predicting missing entries of a matrix, from a subset of known entries, is known as \textit{matrix completion}. In today's data-driven world, data completion is essential whether it is the main goal or a pre-processing step.…
We address the inverse problem that arises in compressed sensing of a low-rank matrix. Our approach is to pose the inverse problem as an approximation problem with a specified target rank of the solution. A simple search over the target…
Recent advances in matrix completion enable data imputation in full-rank matrices by exploiting low dimensional (nonlinear) latent structure. In this paper, we develop a new model for high rank matrix completion (HRMC), together with batch…
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…
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…
We study the problem of subspace tracking in the presence of missing data (ST-miss). In recent work, we studied a related problem called robust ST. In this work, we show that a simple modification of our robust ST solution also provably…
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