Kernel Interpolation as a Bayes Point Machine

TL;DR

This paper reveals that kernel interpolation functions as a Bayes point machine, enabling new theoretical insights into generalization in neural networks through ensemble and convex geometry theories.

Contribution

It establishes that kernel interpolation is a Bayes point machine for Gaussian process classification, linking ensemble theory and convex geometry to neural network generalization.

Findings

Kernel interpolation acts as a Bayes point machine.

Large margin neural networks behave like Bayes point machines.

Derived PAC-Bayes risk bounds for kernel interpolation.

Abstract

A Bayes point machine is a single classifier that approximates the majority decision of an ensemble of classifiers. This paper observes that kernel interpolation is a Bayes point machine for Gaussian process classification. This observation facilitates the transfer of results from both ensemble theory as well as an area of convex geometry known as Brunn-Minkowski theory to derive PAC-Bayes risk bounds for kernel interpolation. Since large margin, infinite width neural networks are kernel interpolators, the paper's findings may help to explain generalisation in neural networks more broadly. Supporting this idea, the paper finds evidence that large margin, finite width neural networks behave like Bayes point machines too.