Gaussian Processes on Graphs via Spectral Kernel Learning

TL;DR

This paper introduces a spectral kernel learning method for Gaussian processes on graphs, enabling adaptive, interpretable predictions without eigen-decomposition, and demonstrates superior performance on synthetic and real data.

Contribution

It presents a novel spectral kernel learning approach for Gaussian processes on graphs that is both interpretable and computationally efficient by avoiding eigen-decomposition.

Findings

Accurately recovers ground truth spectral filters in synthetic experiments.

Achieves superior prediction performance on real-world graph data.

Enables flexible modeling of various graph signal structures.

Abstract

We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible polynomial function in the graph spectral domain. Unlike most existing approaches, we propose to learn such a spectral kernel, where the polynomial setup enables learning without the need for eigen-decomposition of the graph Laplacian. In addition, this kernel has the interpretability of graph filtering achieved by a bespoke maximum likelihood learning algorithm that enforces the positivity of the spectrum. We demonstrate the interpretability of the model in synthetic experiments from which we show the various ground truth spectral filters can be accurately recovered, and the adaptability translates to superior performances in the prediction of real-world graph data of various characteristics.