تقرير
Nystr\'om Kernel Mean Embeddings
| العنوان: | Nystr\'om Kernel Mean Embeddings |
|---|---|
| المؤلفون: | Chatalic, Antoine, Schreuder, Nicolas, Rudi, Alessandro, Rosasco, Lorenzo |
| المصدر: | ICML 2022 |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science Statistics |
| مصطلحات موضوعية: | Statistics - Machine Learning, Computer Science - Machine Learning |
| الوصف: | Kernel mean embeddings are a powerful tool to represent probability distributions over arbitrary spaces as single points in a Hilbert space. Yet, the cost of computing and storing such embeddings prohibits their direct use in large-scale settings. We propose an efficient approximation procedure based on the Nystr\"om method, which exploits a small random subset of the dataset. Our main result is an upper bound on the approximation error of this procedure. It yields sufficient conditions on the subsample size to obtain the standard $n^{-1/2}$ rate while reducing computational costs. We discuss applications of this result for the approximation of the maximum mean discrepancy and quadrature rules, and illustrate our theoretical findings with numerical experiments. Comment: 8 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2201.13055 |
| رقم الأكسشن: | edsarx.2201.13055 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |