On the Probabilistic Approximation in Reproducing Kernel Hilbert Spaces

• Published in: arXiv.org
• Main Authors: Chen, Dongwei, Wang, Kai-Hsiang
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 18.09.2024
• Subjects: Approximation; Hilbert space; Probability theory; Statistical analysis; Uniqueness theorems

This paper generalizes the least square method to probabilistic approximation in reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer. Furthermore, we generalize the celebrated representer theorem in this setting, and especially when the probability measure is fin...