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Count-sketch is a popular matrix sketching algorithm that can produce a sketch of an input data matrix X in O(nnz(X))time where nnz(X) denotes the number of non-zero entries in X. The sketched matrix will be much smaller than X while…

Machine Learning · Computer Science 2020-11-30 Yuhan Wang , Zijian Lei , Liang Lan

We introduce SketchGNN, a convolutional graph neural network for semantic segmentation and labeling of freehand vector sketches. We treat an input stroke-based sketch as a graph, with nodes representing the sampled points along input…

Computer Vision and Pattern Recognition · Computer Science 2021-03-26 Lumin Yang , Jiajie Zhuang , Hongbo Fu , Xiangzhi Wei , Kun Zhou , Youyi Zheng

In this paper, we propose and study a technique to reduce the number of parameters and computation time in convolutional neural networks. We use Kronecker product to exploit the local structures within convolution and fully-connected…

Computer Vision and Pattern Recognition · Computer Science 2016-02-05 Shuchang Zhou , Jia-Nan Wu , Yuxin Wu , Xinyu Zhou

We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…

Numerical Analysis · Mathematics 2021-05-05 Misha E. Kilmer , Arvind K. Saibaba

The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two…

Numerical Analysis · Mathematics 2023-06-12 Rachel Minster , Zitong Li , Grey Ballard

To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…

Data Structures and Algorithms · Computer Science 2020-07-15 David P. Woodruff , Amir Zandieh

We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a…

Machine Learning · Computer Science 2019-12-13 Xiaofei Shi , David P. Woodruff

We consider sketching algorithms which first quickly compress data by multiplication with a random sketch matrix, and then apply the sketch to quickly solve an optimization problem, e.g., low rank approximation. In the learning-based…

Machine Learning · Computer Science 2021-06-08 Simin Liu , Tianrui Liu , Ali Vakilian , Yulin Wan , David P. Woodruff

The Neural Tangent Kernel (NTK) characterizes the behavior of infinitely-wide neural networks trained under least squares loss by gradient descent. Recent works also report that NTK regression can outperform finitely-wide neural networks…

Machine Learning · Computer Science 2021-12-09 Amir Zandieh , Insu Han , Haim Avron , Neta Shoham , Chaewon Kim , Jinwoo Shin

Pairwise learning corresponds to the supervised learning setting where the goal is to make predictions for pairs of objects. Prominent applications include predicting drug-target or protein-protein interactions, or customer-product…

Machine Learning · Computer Science 2024-10-24 Markus Viljanen , Antti Airola , Tapio Pahikkala

Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be…

Data Structures and Algorithms · Computer Science 2021-08-24 Zhao Song , David P. Woodruff , Zheng Yu , Lichen Zhang

Sketching is a dimensionality reduction technique where one compresses a matrix by linear combinations that are chosen at random. A line of work has shown how to sketch the Hessian to speed up each iteration in a second order method, but…

Machine Learning · Computer Science 2021-10-07 Yi Li , Honghao Lin , David P. Woodruff

Dot product kernels, such as polynomial and exponential (softmax) kernels, are among the most widely used kernels in machine learning, as they enable modeling the interactions between input features, which is crucial in applications like…

Machine Learning · Statistics 2024-08-14 Jonas Wacker , Motonobu Kanagawa , Maurizio Filippone

Space-efficient streaming estimation of quantiles in massive datasets is a fundamental problem with numerous applications in data monitoring and analysis. While theoretical research led to optimal algorithms, such as the Greenwald-Khanna…

Data Structures and Algorithms · Computer Science 2025-09-12 Aleksander Łukasiewicz , Jakub Tětek , Pavel Veselý

Tensor train decomposition is one of the most powerful approaches for processing high-dimensional data. For low-rank tensor train decomposition of large tensors, the alternating least squares (ALS) algorithm is widely used by updating each…

Numerical Analysis · Mathematics 2023-09-18 Zhongming Chen , Huilin Jiang , Gaohang Yu , Liqun Qi

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 present efficient, sketching-based methods for the summation of tensors in Tucker format. Leveraging the algebraic structure of Khatri-Rao and Kronecker products, our approach enables compressed arithmetic on Tucker tensors while…

Large tensors are frequently encountered in various fields such as computer vision, scientific simulations, sensor networks, and data mining. However, these tensors are often too large for convenient processing, transfer, or storage.…

Optimization and Control · Mathematics 2024-09-26 Zhiguang Cheng , Gaohang Yu , Xiaohao Cai , Liqun Qi

By leveraging the kernel trick in the output space, kernel-induced losses provide a principled way to define structured output prediction tasks for a wide variety of output modalities. In particular, they have been successfully used in the…

Machine Learning · Statistics 2024-06-14 Tamim El Ahmad , Junjie Yang , Pierre Laforgue , Florence d'Alché-Buc

In this paper, we investigate effective sketching schemes via sparsification for high dimensional multilinear arrays or tensors. More specifically, we propose a novel tensor sparsification algorithm that retains a subset of the entries of a…

Methodology · Statistics 2017-11-17 Dong Xia , Ming Yuan