Fast Summation of Radial Kernels via QMC Slicing
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916626510643200 |
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| author | Hertrich, Johannes Jahn, Tim Quellmalz, Michael |
| author_facet | Hertrich, Johannes Jahn, Tim Quellmalz, Michael |
| contents | The fast computation of large kernel sums is a challenging task, which arises as a subproblem in any kernel method. We approach the problem by slicing, which relies on random projections to one-dimensional subspaces and fast Fourier summation. We prove bounds for the slicing error and propose a quasi-Monte Carlo (QMC) approach for selecting the projections based on spherical quadrature rules. Numerical examples demonstrate that our QMC-slicing approach significantly outperforms existing methods like (QMC-)random Fourier features, orthogonal Fourier features or non-QMC slicing on standard test datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01316 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast Summation of Radial Kernels via QMC Slicing Hertrich, Johannes Jahn, Tim Quellmalz, Michael Numerical Analysis Machine Learning Computation The fast computation of large kernel sums is a challenging task, which arises as a subproblem in any kernel method. We approach the problem by slicing, which relies on random projections to one-dimensional subspaces and fast Fourier summation. We prove bounds for the slicing error and propose a quasi-Monte Carlo (QMC) approach for selecting the projections based on spherical quadrature rules. Numerical examples demonstrate that our QMC-slicing approach significantly outperforms existing methods like (QMC-)random Fourier features, orthogonal Fourier features or non-QMC slicing on standard test datasets. |
| title | Fast Summation of Radial Kernels via QMC Slicing |
| topic | Numerical Analysis Machine Learning Computation |
| url | https://arxiv.org/abs/2410.01316 |