The Orthogonal Polynomial Approximation in the Reproducing Kernel Hilbert Space
Time: 2023-05-18
Published By: He Liu
Speaker(s): He Zhang(PKU)
Time: 16:00-17:30 May 21, 2023
Venue: Room 77201, Jingchunyuan 78, BICMR
The reproducing kernel Hilbert space (RKHS) is a particular class of Hilbert space satisfying the reproducing property. All its elements yield similar properties to the corresponding kernel, e.g., regularity and decay rate. My talk will revisit the orthogonal polynomial approximation using an RKHS setup, including
1. construct kernels and RKHS via orthogonal polynomials,2. discuss the universality (denseness in the continuous function spaces) of the resulting RKHS,
3. study the approximation error, and
4. guide in choosing the hypothesis spaces for statistical learning problems.
My talk will briefly introduce the RKHS theory, including the famous Mercer's theorem, and show application examples in density function estimation and Polynomial Chaos expansion.
