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This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…

Numerical Analysis · Computer Science 2018-01-03 Joel A. Tropp , Alp Yurtsever , Madeleine Udell , Volkan Cevher

We study graph computations in an enhanced data streaming setting, where a space-bounded client reading the edge stream of a massive graph may delegate some of its work to a cloud service. We seek algorithms that allow the client to verify…

Data Structures and Algorithms · Computer Science 2020-07-08 Amit Chakrabarti , Prantar Ghosh , Justin Thaler

Coverage problems are central in optimization and have a wide range of applications in data mining and machine learning. While several distributed algorithms have been developed for coverage problems, the existing methods suffer from…

Data Structures and Algorithms · Computer Science 2017-03-13 MohammadHossein Bateni , Hossein Esfandiari , Vahab Mirrokni

We give two provably accurate feature-selection techniques for the linear SVM. The algorithms run in deterministic and randomized time respectively. Our algorithms can be used in an unsupervised or supervised setting. The supervised…

Machine Learning · Statistics 2015-02-09 Saurabh Paul , Malik Magdon-Ismail , Petros Drineas

This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…

Data Structures and Algorithms · Computer Science 2015-02-11 David P. Woodruff

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…

Statistics Theory · Mathematics 2015-02-03 Olga Klopp

Sketching is one of the most fundamental tools in large-scale machine learning. It enables runtime and memory saving via randomly compressing the original large problem into lower dimensions. In this paper, we propose a novel sketching…

Machine Learning · Computer Science 2023-06-08 Zhao Song , Yitan Wang , Zheng Yu , Lichen Zhang

Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…

Computer Vision and Pattern Recognition · Computer Science 2020-10-22 Huu Le , Christopher Zach , Edward Rosten , Oliver J. Woodford

Aiming to provide a faster and convenient truncated SVD algorithm for large sparse matrices from real applications (i.e. for computing a few of largest singular values and the corresponding singular vectors), a dynamically shifted power…

Mathematical Software · Computer Science 2024-04-16 Xu Feng , Wenjian Yu , Yuyang Xie , Jie Tang

Given a symmetric matrix $A$, we show from the simple sketch $GAG^T$, where $G$ is a Gaussian matrix with $k = O(1/\epsilon^2)$ rows, that there is a procedure for approximating all eigenvalues of $A$ simultaneously to within $\epsilon…

Data Structures and Algorithms · Computer Science 2023-04-20 William Swartworth , David P. Woodruff

We propose OverSketch, an approximate algorithm for distributed matrix multiplication in serverless computing. OverSketch leverages ideas from matrix sketching and high-performance computing to enable cost-efficient multiplication that is…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-02-25 Vipul Gupta , Shusen Wang , Thomas Courtade , Kannan Ramchandran

This paper describes Sparse Frequent Directions, a variant of Frequent Directions for sketching sparse matrices. It resembles the original algorithm in many ways: both receive the rows of an input matrix $A^{n \times d}$ one by one in the…

Data Structures and Algorithms · Computer Science 2016-02-18 Mina Ghashami , Edo Liberty , Jeff M. Phillips

We consider the problem of reconstructing the symmetric difference between similar sets from their representations (sketches) of size linear in the number of differences. Exact solutions to this problem are based on error-correcting coding…

Data Structures and Algorithms · Computer Science 2024-04-16 Djamal Belazzougui , Gregory Kucherov , Stefan Walzer

We propose a novel method for speeding up stochastic optimization algorithms via sketching methods, which recently became a powerful tool for accelerating algorithms for numerical linear algebra. We revisit the method of conditioning for…

Numerical Analysis · Computer Science 2015-06-10 Alon Gonen , Shai Shalev-Shwartz

We consider a streaming data model in which n sensors observe individual streams of data, presented in a turnstile model. Our goal is to analyze the singular value decomposition (SVD) of the matrix of data defined implicitly by the stream…

Information Theory · Computer Science 2012-11-05 Anna C. Gilbert , Jae Young Park , Michael B. Wakin

Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each…

Optimization and Control · Mathematics 2024-02-08 Xufeng Cai , Cheuk Yin Lin , Jelena Diakonikolas

This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…

Numerical Analysis · Mathematics 2023-09-25 Joel A. Tropp , Robert J. Webber

Iterative Hessian sketch (IHS) is an effective sketching method for modeling large-scale data. It was originally proposed by Pilanci and Wainwright (2016; JMLR) based on randomized sketching matrices. However, it is computationally…

Machine Learning · Statistics 2020-03-10 Aijun Zhang , Hengtao Zhang , Guosheng Yin

Sketching is a probabilistic data compression technique that has been largely developed in the computer science community. Numerical operations on big datasets can be intolerably slow; sketching algorithms address this issue by generating a…

Methodology · Statistics 2019-04-04 Daniel Ahfock , William J. Astle , Sylvia Richardson

Momentum Iterative Hessian Sketch (M-IHS) techniques, a group of solvers for large scale regularized linear Least Squares (LS) problems, are proposed and analyzed in detail. Proposed M-IHS techniques are obtained by incorporating the Heavy…

Optimization and Control · Mathematics 2020-12-01 Ibrahim Kurban Ozaslan , Mert Pilanci , Orhan Arikan