Generalized Spectral Kernels

06/07/2015
by   Yves-Laurent Kom Samo, et al.
0

In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary kernels, and propose a family of spectral kernels that extends existing approaches such as spectral mixture kernels and sparse spectrum kernels. Our extension has two primary advantages. Firstly, unlike existing spectral approaches that yield infinite differentiability, the kernels we introduce allow learning the degree of differentiability of the latent function in Gaussian process (GP) models and functions in the reproducing kernel Hilbert space (RKHS) in other kernel methods. Secondly, we show that some of the kernels we propose require fewer parameters than existing spectral kernels for the same accuracy, thereby leading to faster and more robust inference. Finally, we generalize our approach and propose a flexible and tractable family of spectral kernels that we prove can approximate any continuous bounded nonstationary kernel.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/27/2018

Neural Non-Stationary Spectral Kernel

Standard kernels such as Matérn or RBF kernels only encode simple monoto...
research
06/14/2021

Marginalising over Stationary Kernels with Bayesian Quadrature

Marginalising over families of Gaussian Process kernels produces flexibl...
research
07/15/2021

Hida-Matérn Kernel

We present the class of Hida-Matérn kernels, which is the canonical fami...
research
09/07/2009

Kernels for Measures Defined on the Gram Matrix of their Support

We present in this work a new family of kernels to compare positive meas...
research
05/01/2019

High-performance sampling of generic Determinantal Point Processes

Determinantal Point Processes (DPPs) were introduced by Macchi as a mode...
research
12/19/2014

A la Carte - Learning Fast Kernels

Kernel methods have great promise for learning rich statistical represen...
research
07/10/2018

An Empirical Approach For Probing the Definiteness of Kernels

Models like support vector machines or Gaussian process regression often...

Please sign up or login with your details

Forgot password? Click here to reset