相关论文: A multilevel sketch-and-solve method for overdeter…

Randomized subspace embedding methods have had a great impact on the solution of a linear least squares (LS) problem by reducing its row dimension, leading to a randomized or sketched LS (sLS) problem, and use the solution of the sLS…

We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…

For an overdetermined system $\mathsf{A}\mathsf{x} \approx \mathsf{b}$ with $\mathsf{A}$ and $\mathsf{b}$ given, the least-square (LS) formulation $\min_x \, \|\mathsf{A}\mathsf{x}-\mathsf{b}\|_2$ is often used to find an acceptable…

Many learning tasks, such as cross-validation, parameter search, or leave-one-out analysis, involve multiple instances of similar problems, each instance sharing a large part of learning data with the others. We introduce a robust framework…

We propose a novel randomized framework for the estimation problem of large-scale linear statistical models, namely Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), which integrates Sketch-and-Solve and…

Sketch-and-project is a framework which unifies many known iterative methods for solving linear systems and their variants, as well as further extensions to non-linear optimization problems. It includes popular methods such as randomized…

Matrix sketching is a powerful tool for reducing the size of large data matrices. Yet there are fundamental limitations to this size reduction when we want to recover an accurate estimator for a task such as least square regression. We show…

We consider statistical as well as algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. For a LS problem with input data $(X, Y) \in \mathbb{R}^{n \times p} \times \mathbb{R}^n$,…

We consider a least squares regression problem where the data has been generated from a linear model, and we are interested to learn the unknown regression parameters. We consider "sketch-and-solve" methods that randomly project the data…

In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…

Randomized linear system solvers have become popular as they have the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising class of methods, random sketching solvers,…

We consider least-squares problems with quadratic regularization and propose novel sketching-based iterative methods with an adaptive sketch size. The sketch size can be as small as the effective dimension of the data matrix to guarantee…

Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…

Despite being a key bottleneck in many machine learning tasks, the cost of solving large linear systems has proven challenging to quantify due to problem-dependent quantities such as condition numbers. To tackle this, we consider a…

Sketching techniques have gained popularity in numerical linear algebra to accelerate the solution of least squares problems. The so-called $\varepsilon$-subspace embedding property of a sketching matrix $S$ has been largely used to…

In order to compute fast approximations to the singular value decompositions (SVD) of very large matrices, randomized sketching algorithms have become a leading approach. However, a key practical difficulty of sketching an SVD is that the…

Sketching has emerged as a powerful technique for speeding up problems in numerical linear algebra, such as regression. In the overconstrained regression problem, one is given an $n \times d$ matrix $A$, with $n \gg d$, as well as an $n…

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…

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…

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…