Convolutional Gaussian Processes

TL;DR

This paper introduces a convolutional Gaussian process framework that incorporates convolutional structure into Gaussian processes, enabling effective image analysis with improved inference and kernel optimization.

Contribution

It develops an inter-domain inducing point approximation tailored for convolutional kernels, enhancing Gaussian processes for high-dimensional image data.

Findings

Effective application to MNIST and CIFAR-10 datasets.

Kernel combination via marginal likelihood improves performance.

Fast and accurate posterior inference achieved.

Abstract

We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing point approximation that is well-tailored to the convolutional kernel. This allows us to gain the generalisation benefit of a convolutional kernel, together with fast but accurate posterior inference. We investigate several variations of the convolutional kernel, and apply it to MNIST and CIFAR-10, which have both been known to be challenging for Gaussian processes. We also show how the marginal likelihood can be used to find an optimal weighting between convolutional and RBF kernels to further improve performance. We hope that this illustration of the usefulness of a marginal likelihood will help automate discovering architectures in larger models.