Year: 2018
Type: preprint
Abstract: We propose a representation of Gaussian processes (GPs) based on powers of the integral operator defined by a kernel function, we call these stochastic processes integral Gaussian processes (IGPs). Sample paths from IGPs are functions contained within the reproducing kernel Hilbert space (RKHS) defined by the kernel function, in contrast sample paths from the standard GP are not functions within the RKHS. We develop computationally efficient non-parametric regression models based on IGPs. The main innovation in our regression algorithm is the construction of a low dimensional subspace that captures the information most relevant to explaining variation in the response. We use ideas from supervised dimension reduction to compute this subspace. The result of using the construction we propose involves significant improvements in the computational complexity of estimating kernel hyper-parameters as well as reducing the prediction variance.
Source: arXiv (Cornell University)
Authors: Tan, Zilong, Mukherjee, Sayan
Institutions: Carnegie Mellon University, Duke University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2919310405