第45回統計的機械学習セミナー / The 45th Statistical Machine Learning Seminar

Date&Time
2019年6月27日(木)15:00~16:00
/ 27 June, 2019 (Thu) 15:00 - 16:00

Admission Free, No Booking Necessary

Place
統計数理研究所 セミナー室8 (D602)
/ Seminar room8 (D602) @ The Institute of Statistical Mathematics
区切り線
Speaker
Toni Karvonen
(Aalto University, Finland)
Title
Kernel-Based Numerical Integration
Abstract
This talk discusses kernel cubature rules. A kernel cubature rule is a numerical integration method that is worst-case optimal in the reproducing kernel Hilbert space induced by a user-specified positive-definite kernel. An equivalent Gaussian process formulation allows for interpreting kernel cubature rules as probabilistic numerical methods. We review i) non-approximate algorithms based on fully symmetric sets, sparse grids, and shift-invariant kernels that alleviate the characteristic cubic computational cost in the number of data points of kernel-based methods and ii) some connections between kernel cubature and classical polynomial numerical integration methods.