A probabilistic Taylor expansion with Gaussian processes

Toni Karvonen, Jon Cockayne, Filip Tronarp, Simo Särkkä

Abstract: We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consist of derivative evaluations at the expansion point and the prior covariance kernel belongs to the class of Taylor kernels, which can be written in a certain power series form. We discuss and prove some results on maximum likelihood estimation of parameters of Taylor kernels. The proposed framework is a special case of Gaussian process regression based on data that is orthogonal in the reproducing kernel Hilbert space of the covariance kernel.

Submission Length: Long submission (more than 12 pages of main content)

Changes Since Last Submission: Camera ready.

Assigned Action Editor: ~Roman_Garnett1

License: Creative Commons Attribution 4.0 International (CC BY 4.0)

Submission Number: 1287