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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,…

Numerical Analysis · Mathematics 2020-12-23 Vivak Patel , Mohammad Jahangoshahi , Daniel Adrian Maldonado

We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform…

Machine Learning · Computer Science 2020-10-26 Jonathan Lacotte , Mert Pilanci

Projection-based iterative methods for solving large over-determined linear systems are well-known for their simplicity and computational efficiency. It is also known that the correct choice of a sketching procedure (i.e., preprocessing…

Numerical Analysis · Mathematics 2019-12-03 Elizaveta Rebrova , Deanna Needell

We present an approximate algorithm for matrix multiplication based on matrix sketching techniques. First one of the matrix is chosen and sparsified using the online matrix sketching algorithm, and then the matrix product is calculated…

Numerical Analysis · Computer Science 2014-06-12 Huan Wang , Christos Boutsidis , Edo Liberty , Daniel Hsu

In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…

Machine Learning · Statistics 2019-04-05 Miles E. Lopes , Shusen Wang , Michael W. Mahoney

The compressive learning framework reduces the computational cost of training on large-scale datasets. In a sketching phase, the data is first compressed to a lightweight sketch vector, obtained by mapping the data samples through a…

Machine Learning · Statistics 2022-04-20 Vincent Schellekens , Laurent Jacques

Matrix trace estimation is ubiquitous in machine learning applications and has traditionally relied on Hutchinson's method, which requires $O(\log(1/\delta)/\epsilon^2)$ matrix-vector product queries to achieve a $(1 \pm…

Data Structures and Algorithms · Computer Science 2021-11-02 Shuli Jiang , Hai Pham , David P. Woodruff , Qiuyi , Zhang

Matching is one of the most fundamental and broadly applicable problems across many domains. In these diverse real-world applications, there is often a degree of uncertainty in the input which has led to the study of stochastic matching…

Data Structures and Algorithms · Computer Science 2026-04-21 Brian Brubach , Nathaniel Grammel , Will Ma , Calum MacRury , Aravind Srinivasan

We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching…

Statistics Theory · Mathematics 2024-03-21 Pratik Patil , Daniel LeJeune

Accounting for the uncertainty in the predictions of modern neural networks is a challenging and important task in many domains. Existing algorithms for uncertainty estimation require modifying the model architecture and training procedure…

Machine Learning · Statistics 2022-05-09 Alexander Fishkov , Maxim Panov

We revisit the well-studied problem of approximating a matrix product, $\mathbf{A}^T\mathbf{B}$, based on small space sketches $\mathcal{S}(\mathbf{A})$ and $\mathcal{S}(\mathbf{B})$ of $\mathbf{A} \in \R^{n \times d}$ and $\mathbf{B}\in…

Data Structures and Algorithms · Computer Science 2025-01-30 Majid Daliri , Juliana Freire , Danrong Li , Christopher Musco

SKETCHVERIFY is a within-tier cost-performance policy, not a universal accuracy improvement. The operational question: a practitioner stuck with a small, cheap code model (here, Gemini 3.1 Flash Lite) for latency, deployment, or budget…

Machine Learning · Computer Science 2026-05-12 Shan Jiang , Zijian Yi , Chenguang Zhu

Constrained least squares problems arise in many applications. Their memory and computation costs are expensive in practice involving high-dimensional input data. We employ the so-called "sketching" strategy to project the least squares…

Optimization and Control · Mathematics 2021-09-07 Ke Chen , Ruhui Jin

The power of randomized algorithms in numerical methods have led to fast solutions which use the Singular Value Decomposition (SVD) as a core routine. However, given the large data size of modern and the modest runtime of SVD, most…

Machine Learning · Computer Science 2018-12-20 Hui Han Chin , Paul Pu Liang

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…

Statistics Theory · Mathematics 2019-10-08 Edgar Dobriban , Sifan Liu

We undertake a systematic study of sketching a quadratic form: given an $n \times n$ matrix $A$, create a succinct sketch $\textbf{sk}(A)$ which can produce (without further access to $A$) a multiplicative $(1+\epsilon)$-approximation to…

Data Structures and Algorithms · Computer Science 2026-02-23 Alexandr Andoni , Jiecao Chen , Robert Krauthgamer , Bo Qin , David P. Woodruff , Qin Zhang

We consider distributed optimization methods for problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We leverage randomized sketches for reducing the problem dimensions as well as…

Optimization and Control · Mathematics 2022-03-21 Burak Bartan , Mert Pilanci

Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…

Numerical Analysis · Mathematics 2016-12-20 Robert M. Gower

Iterative sketching and sketch-and-precondition are well-established randomized algorithms for solving large-scale, over-determined linear least-squares problems. In this paper, we introduce a new perspective that interprets Iterative…

Numerical Analysis · Mathematics 2024-10-18 Ruihan Xu , Yiping Lu

Matrix sketching, aimed at approximating a matrix $\boldsymbol{A} \in \mathbb{R}^{N\times d}$ consisting of vector streams of length $N$ with a smaller sketching matrix $\boldsymbol{B} \in \mathbb{R}^{\ell\times d}, \ell \ll N$, has…

Databases · Computer Science 2024-11-06 Hanyan Yin , Dongxie Wen , Jiajun Li , Zhewei Wei , Xiao Zhang , Zengfeng Huang , Feifei Li