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Linear regression is a classic method of data analysis. In recent years, sketching -- a method of dimension reduction using random sampling, random projections, or both -- has gained popularity as an effective computational approximation…

Machine Learning · Statistics 2020-08-04 Jocelyn T. Chi , Ilse C. F. Ipsen

Scalable algorithms to solve optimization and regression tasks even approximately, are needed to work with large datasets. In this paper we study efficient techniques from matrix sketching to solve a variety of convex constrained regression…

Machine Learning · Computer Science 2019-11-01 Graham Cormode , Charlie Dickens

Sketched gradient algorithms have been recently introduced for efficiently solving the large-scale constrained Least-squares regressions. In this paper we provide novel convergence analysis for the basic method {\it Gradient Projection…

Optimization and Control · Mathematics 2017-06-05 Junqi Tang , Mohammad Golbabaee , Mike Davies

We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that…

Optimization and Control · Mathematics 2015-05-12 Mert Pilanci , Martin J. Wainwright

Iterative sketching and sketch-and-precondition are randomized algorithms used for solving overdetermined linear least-squares problems. When implemented in exact arithmetic, these algorithms produce high-accuracy solutions to least-squares…

Numerical Analysis · Mathematics 2024-04-15 Ethan N. Epperly

A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct…

Numerical Analysis · Mathematics 2022-03-25 Oleg Balabanov , Anthony Nouy

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

We investigate iterative methods with randomized preconditioners for solving overdetermined least-squares problems, where the preconditioners are based on a random embedding of the data matrix. We consider two distinct approaches: the…

Numerical Analysis · Mathematics 2021-04-15 Jonathan Lacotte , Mert Pilanci

This article focuses on drawing computationally-efficient predictive inference from Gaussian process (GP) regressions with a large number of features when the response is conditionally independent of the features given the projection to a…

Methodology · Statistics 2024-09-27 Samuel Gailliot , Rajarshi Guhaniyogi , Roger D. Peng

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

We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…

Optimization and Control · Mathematics 2021-05-18 Jonathan Lacotte , Yifei Wang , Mert Pilanci

Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…

Optimization and Control · Mathematics 2020-10-26 Jonathan Lacotte , Sifan Liu , Edgar Dobriban , Mert Pilanci

In this paper, combining count sketch and maximal weighted residual Kaczmarz method, we propose a fast randomized algorithm for large overdetermined linear systems. Convergence analysis of the new algorithm is provided. Numerical…

Numerical Analysis · Mathematics 2020-04-07 Yanjun Zhang , Hanyu Li

Leveraging the kernel trick in both the input and output spaces, surrogate kernel methods are a flexible and theoretically grounded solution to structured output prediction. If they provide state-of-the-art performance on complex data sets…

Machine Learning · Statistics 2024-05-07 Tamim El Ahmad , Luc Brogat-Motte , Pierre Laforgue , Florence d'Alché-Buc

Recently, Bessa et al. (PODS 2023) showed that sketches based on coordinated weighted sampling theoretically and empirically outperform popular linear sketching methods like Johnson-Lindentrauss projection and CountSketch for the ubiquitous…

Databases · Computer Science 2024-08-23 Majid Daliri , Juliana Freire , Christopher Musco , Aécio Santos , Haoxiang Zhang

Learning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. We propose a "compressive learning" framework where we estimate model parameters from a sketch of the training data. This sketch…

Machine Learning · Computer Science 2017-05-08 Nicolas Keriven , Anthony Bourrier , Rémi Gribonval , Patrick Pérez

This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and…

Optimization and Control · Mathematics 2021-12-09 Han Wang , James Anderson

Randomized iterative methods, such as the randomized Kaczmarz method, have gained significant attention for solving large-scale linear systems due to their simplicity and efficiency. Meanwhile, Krylov subspace methods have emerged as a…

Numerical Analysis · Mathematics 2025-05-28 Yonghan Sun , Deren Han , Jiaxin Xie

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

For tensor linear systems with respect to the popular t-product, we first present the sketch-and-project method and its adaptive variants. Their Fourier domain versions are also investigated. Then, considering that the existing sketching…

Numerical Analysis · Mathematics 2022-03-30 Ling Tang , Yajie Yu , Yanjun Zhang , Hanyu Li