Related papers: Topics in Matrix Sampling Algorithms

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…

A conditional sampling oracle for a probability distribution D returns samples from the conditional distribution of D restricted to a specified subset of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et al. 2014)…

We consider the related tasks of matrix completion and matrix approximation from missing data and propose adaptive sampling procedures for both problems. We show that adaptive sampling allows one to eliminate standard incoherence…

We study the problem of learning a structured approximation (low-rank, sparse, banded, etc.) to an unknown matrix $A$ given access to matrix-vector product (matvec) queries of the form $x \rightarrow Ax$ and $x \rightarrow A^Tx$. This…

Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…

A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select…

he segment minimization problem consists of finding the smallest set of integer matrices that sum to a given intensity matrix, such that each summand has only one non-zero value, and the non-zeroes in each row are consecutive. This has…

We develop algorithms for inner approximating the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and…

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…

There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which…

In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at…

Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from…

We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…

While leverage score sampling provides powerful tools for approximating solutions to large least squares problems, the cost of computing exact scores and sampling often prohibits practical application. This paper addresses this challenge by…

We address the subset selection problem for matrices, where the goal is to select a subset of $k$ columns from a "short-and-fat" matrix $X \in \mathbb{R}^{m \times n}$, such that the pseudoinverse of the sampled submatrix has as small…

We consider the problem of selecting the best subset of exactly $k$ columns from an $m \times n$ matrix $A$. We present and analyze a novel two-stage algorithm that runs in $O(\min\{mn^2,m^2n\})$ time and returns as output an $m \times k$…

The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…

We prove that for any real-valued matrix $X \in \R^{m \times n}$, and positive integers $r \ge k$, there is a subset of $r$ columns of $X$ such that projecting $X$ onto their span gives a $\sqrt{\frac{r+1}{r-k+1}}$-approximation to best…

Low rank model arises from a wide range of applications, including machine learning, signal processing, computer algebra, computer vision, and imaging science. Low rank matrix recovery is about reconstructing a low rank matrix from…