Local Random Feature Approximations of the Gaussian Kernel
- URL: http://arxiv.org/abs/2204.05667v1
- Date: Tue, 12 Apr 2022 09:52:36 GMT
- Title: Local Random Feature Approximations of the Gaussian Kernel
- Authors: Jonas Wacker, Maurizio Filippone
- Abstract summary: We focus on the popular Gaussian kernel and on techniques to linearize kernel-based models by means of random feature approximations.
We show that such approaches yield poor results when modelling high-frequency data, and we propose a novel localization scheme that improves kernel approximations and downstream performance significantly.
- Score: 14.230653042112834
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A fundamental drawback of kernel-based statistical models is their limited
scalability to large data sets, which requires resorting to approximations. In
this work, we focus on the popular Gaussian kernel and on techniques to
linearize kernel-based models by means of random feature approximations. In
particular, we do so by studying a less explored random feature approximation
based on Maclaurin expansions and polynomial sketches. We show that such
approaches yield poor results when modelling high-frequency data, and we
propose a novel localization scheme that improves kernel approximations and
downstream performance significantly in this regime. We demonstrate these gains
on a number of experiments involving the application of Gaussian process
regression to synthetic and real-world data of different data sizes and
dimensions.
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