pylspack:绘制、列子集选择、回归和杠杆分数的并行算法和数据结构

IF 2.7 1区 数学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING
Aleksandros Sobczyk, Efstratios Gallopoulos
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引用次数: 3

摘要

我们提出了数值线性代数中三种基本运算的并行算法和数据结构:(i)高斯和CountSketch随机投影及其组合,(ii)Gram矩阵的计算,以及(iii)两个矩阵乘积的平方行范数的计算,特别关注在许多应用中出现的“高和瘦”矩阵。我们详细分析了无处不在的CountSketch变换及其与高斯随机投影的结合,考虑了内存需求、计算复杂性和工作负载平衡。我们还演示了如何将这些结果应用于列子集选择、最小二乘回归和杠杆分数计算。这些工具已经在pylspack中实现,pylspack是一个公开的Python包1,其核心是用C++编写的,并与OpenMP并行,与SciPy和NumPy的标准矩阵数据结构兼容。大量的数值实验表明,所提出的算法具有良好的扩展性,并且显著优于现有的高矩阵和瘦矩阵库。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
pylspack: Parallel Algorithms and Data Structures for Sketching, Column Subset Selection, Regression, and Leverage Scores
We present parallel algorithms and data structures for three fundamental operations in Numerical Linear Algebra: (i) Gaussian and CountSketch random projections and their combination, (ii) computation of the Gram matrix, and (iii) computation of the squared row norms of the product of two matrices, with a special focus on “tall-and-skinny” matrices, which arise in many applications. We provide a detailed analysis of the ubiquitous CountSketch transform and its combination with Gaussian random projections, accounting for memory requirements, computational complexity and workload balancing. We also demonstrate how these results can be applied to column subset selection, least squares regression and leverage scores computation. These tools have been implemented in pylspack, a publicly available Python package1 whose core is written in C++ and parallelized with OpenMP and that is compatible with standard matrix data structures of SciPy and NumPy. Extensive numerical experiments indicate that the proposed algorithms scale well and significantly outperform existing libraries for tall-and-skinny matrices.
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来源期刊
ACM Transactions on Mathematical Software
ACM Transactions on Mathematical Software 工程技术-计算机:软件工程
CiteScore
5.00
自引率
3.70%
发文量
50
审稿时长
>12 weeks
期刊介绍: As a scientific journal, ACM Transactions on Mathematical Software (TOMS) documents the theoretical underpinnings of numeric, symbolic, algebraic, and geometric computing applications. It focuses on analysis and construction of algorithms and programs, and the interaction of programs and architecture. Algorithms documented in TOMS are available as the Collected Algorithms of the ACM at calgo.acm.org.
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