Year: 2023
Type: preprint
Abstract: We apply the discrepancy method and a chaining approach to give improved bounds on the coreset complexity of a wide class of kernel functions. Our results give randomized polynomial time algorithms to produce coresets of size $O\big(\frac{\sqrt{d}}{\varepsilon}\sqrt{\log\log \frac{1}{\varepsilon}}\big)$ for the Gaussian and Laplacian kernels in the case that the data set is uniformly bounded, an improvement that was not possible with previous techniques. We also obtain coresets of size $O\big(\frac{1}{\varepsilon}\sqrt{\log\log \frac{1}{\varepsilon}}\big)$ for the Laplacian kernel for $d$ constant. Finally, we give the best known bounds of $O\big(\frac{\sqrt{d}}{\varepsilon}\sqrt{\log(2\max\{1,α\})}\big)$ on the coreset complexity of the exponential, Hellinger, and JS Kernels, where $1/α$ is the bandwidth parameter of the kernel.
Source: arXiv (Cornell University)
Authors: Bozzai, Rainie, Rothvoss, Thomas
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4387635916