A Theoretical Framework for Bayesian Nonparametric Regression: Orthonormal Random Series and Rates of Contraction
Year: 2017
Type: preprint
Abstract: We develop a unifying framework for Bayesian nonparametric regression to study the rates of contraction with respect to the integrated $L_2$-distance without assuming the regression function space to be uniformly bounded. The framework is built upon orthonormal random series in a flexible manner. A general theorem for deriving rates of contraction for Bayesian nonparametric regression is provided under the proposed framework. As specific applications, we obtain the near-parametric rate of contraction for the squared-exponential Gaussian process when the true function is analytic, the adaptive rates of contraction for the sieve prior, and the adaptive-and-exact rates of contraction for the un-modified block prior when the true function is {\alpha}-smooth. Extensions to wavelet series priors and fixed-design regression problems are also discussed.
Source: arXiv (Cornell University)
Authors: Fangzheng Xie, Wei Jin, Yanxun Xu
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2775083283