Gaussian Processes on Graphs via Spectral Kernel Learning
This work addresses the need for adaptive and interpretable graph signal prediction methods, though it appears incremental as it builds on existing spectral approaches with a novel learning technique.
The authors tackled the problem of predicting signals on graph nodes by proposing a Gaussian process with a spectral kernel that learns a flexible polynomial in the graph spectral domain, resulting in accurate recovery of ground truth filters and superior prediction performance on real-world graph data.
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.