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Related papers: Learning-Augmented Sketches for Hessians

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Recently, sketches have been introduced as a general language for representing the subgoal structure of instances drawn from the same domain. Sketches are collections of rules of the form C -> E over a given set of features where C…

Artificial Intelligence · Computer Science 2022-03-29 Dominik Drexler , Jendrik Seipp , Hector Geffner

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…

Numerical Analysis · Mathematics 2020-06-04 Ke Chen , Qin Li , Kit Newton , Steve Wright

We propose a randomized first order optimization method--SEGA (SkEtched GrAdient method)-- which progressively throughout its iterations builds a variance-reduced estimate of the gradient from random linear measurements (sketches) of the…

Optimization and Control · Mathematics 2018-10-19 Filip Hanzely , Konstantin Mishchenko , Peter Richtarik

Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…

Data Structures and Algorithms · Computer Science 2025-05-20 Ninh Pham , Rasmus Pagh

The power method is one of the most fundamental tools for extracting top principal components from data through low-rank matrix approximation. Yet, when the target rank is large, the cost of matrix multiplication associated with this…

Numerical Analysis · Mathematics 2026-05-12 Shabarish Chenakkod , Michał Dereziński

We propose a multi-scale multi-channel deep neural network framework that, for the first time, yields sketch recognition performance surpassing that of humans. Our superior performance is a result of explicitly embedding the unique…

Computer Vision and Pattern Recognition · Computer Science 2015-07-22 Qian Yu , Yongxin Yang , Yi-Zhe Song , Tao Xiang , Timothy Hospedales

Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is…

Data Structures and Algorithms · Computer Science 2020-12-23 Thomas D. Ahle , Michael Kapralov , Jakob B. T. Knudsen , Rasmus Pagh , Ameya Velingker , David Woodruff , Amir Zandieh

Given a persistence diagram with $n$ points, we give an algorithm that produces a sequence of $n$ persistence diagrams converging in bottleneck distance to the input diagram, the $i$th of which has $i$ distinct (weighted) points and is a…

Computational Geometry · Computer Science 2020-12-04 Donald R. Sheehy , Siddharth Sheth

We propose a deep hashing framework for sketch retrieval that, for the first time, works on a multi-million scale human sketch dataset. Leveraging on this large dataset, we explore a few sketch-specific traits that were otherwise…

Computer Vision and Pattern Recognition · Computer Science 2018-04-05 Peng Xu , Yongye Huang , Tongtong Yuan , Kaiyue Pang , Yi-Zhe Song , Tao Xiang , Timothy M. Hospedales , Zhanyu Ma , Jun Guo

In this work, we propose a method for speeding up linear regression distributively, while ensuring security. We leverage randomized sketching techniques, and improve straggler resilience in asynchronous systems. Specifically, we apply a…

Information Theory · Computer Science 2022-02-23 Neophytos Charalambides , Hessam Mahdavifar , Mert Pilanci , Alfred O. Hero

In this paper we show that for the purposes of dimensionality reduction certain class of structured random matrices behave similarly to random Gaussian matrices. This class includes several matrices for which matrix-vector multiply can be…

Information Theory · Computer Science 2015-10-08 Samet Oymak , Benjamin Recht , Mahdi Soltanolkotabi

We propose a novel image-to-pencil translation method that could not only generate high-quality pencil sketches but also offer the drawing process. Existing pencil sketch algorithms are based on texture rendering rather than the direct…

Computer Vision and Pattern Recognition · Computer Science 2020-12-17 Zhengyan Tong , Xuanhong Chen , Bingbing Ni , Xiaohang Wang

We develop an algorithm for estimating the values of a vector x in R^n over a support S of size k from a randomized sparse binary linear sketch Ax of size O(k). Given Ax and S, we can recover x' with ||x' - x_S||_2 <= eps ||x - x_S||_2 with…

Data Structures and Algorithms · Computer Science 2010-11-22 Eric Price

Recent advancement of the WWW, IOT, social network, e-commerce, etc. have generated a large volume of data. These datasets are mostly represented by high dimensional and sparse datasets. Many fundamental subroutines of common data analytic…

Information Retrieval · Computer Science 2019-10-11 Rameshwar Pratap , Debajyoti Bera , Karthik Revanuru

We address the statistical and optimization impacts of the classical sketch and Hessian sketch used to approximately solve the Matrix Ridge Regression (MRR) problem. Prior research has quantified the effects of classical sketch on the…

Machine Learning · Statistics 2018-05-08 Shusen Wang , Alex Gittens , Michael W. Mahoney

The aim of this paper is two-fold: firstly, to present subspace embedding properties for $s$-hashing sketching matrices, with $s\geq 1$, that are optimal in the projection dimension $m$ of the sketch, namely, $m=\mathcal{O}(d)$, where $d$…

Numerical Analysis · Mathematics 2021-05-26 Coralia Cartis , Jan Fiala , Zhen Shao

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

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…

Optimization and Control · Mathematics 2016-02-29 Farbod Roosta-Khorasani , Michael W. Mahoney

Many real-world matrix datasets arrive as high-throughput vector streams, making it impractical to store or process them in their entirety. To enable real-time analytics under limited computational, memory, and communication resources,…

Databases · Computer Science 2026-01-12 Hanyan Yin , Dongxie Wen , Jiajun Li , Zhewei Wei , Xiao Zhang , Peng Zhao , Zhi-Hua Zhou

Distance computation is one of the most fundamental primitives used in communication networks. The cost of effectively and accurately computing pairwise network distances can become prohibitive in large-scale networks such as the Internet…

Data Structures and Algorithms · Computer Science 2011-12-07 Atish Das Sarma , Michael Dinitz , Gopal Pandurangan