Related papers: A note on column subset selection
Given a set (or multiset) S of n numbers and a target number t, the subset sum problem is to decide if there is a subset of S that sums up to t. There are several methods for solving this problem, including exhaustive search,…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…
We consider a fashion discounter that supplies any of its many branches with an integral multiple of lots whose size assortment structure stems from a set of many applicable lot-types. We design a column generation algorithm for the optimal…
A common problem in large-scale data analysis is to approximate a matrix using a combination of specifically sampled rows and columns, known as CUR decomposition. Unfortunately, in many real-world environments, the ability to sample…
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…
In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the…
Randomization is a fundamental tool used in many theoretical and practical areas of computer science. We study here the role of randomization in the area of submodular function maximization. In this area most algorithms are randomized, and…
We consider low-rank reconstruction of a matrix using its columns and we present asymptotically optimal algorithms for both spectral norm and Frobenius norm reconstruction. The main tools we introduce to obtain our r esults are: (i) the use…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
The maximum volume $j$-simplex problem asks to compute the $j$-dimensional simplex of maximum volume inside the convex hull of a given set of $n$ points in $\mathbb{Q}^d$. We give a deterministic approximation algorithm for this problem…
We consider the problem of selecting a small subset of representative variables from a large dataset. In the computer science literature, this dimensionality reduction problem is typically formalized as Column Subset Selection (CSS).…
We compute a \emph{sparse} solution to the classical least-squares problem $\min_x||A x -b||,$ where $A$ is an arbitrary matrix. We describe a novel algorithm for this sparse least-squares problem. The algorithm operates as follows: first,…
We consider a variety of criteria for selecting k representative columns from a real mxn matrix A, when sufficiently few columns are required, i.e., 1<= k<= min{rank(A), m/3}. The criteria include the following optimization problems:…
We study three fundamental problems of Linear Algebra, lying in the heart of various Machine Learning applications, namely: 1)"Low-rank Column-based Matrix Approximation". We are given a matrix A and a target rank k. The goal is to select a…
In this paper, we investigate the randomized algorithms for block matrix multiplication from random sampling perspective. Based on the A-optimal design criterion, the optimal sampling probabilities and sampling block sizes are obtained. To…
Recently, there has been much interest in finding globally optimal Bayesian network structures. These techniques were developed for generative scores and can not be directly extended to discriminative scores, as desired for classification.…
The NP-hard Distinct Vectors problem asks to delete as many columns as possible from a matrix such that all rows in the resulting matrix are still pairwise distinct. Our main result is that, for binary matrices, there is a complexity…