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Gaussian Processes on Graphs via Spectral Kernel Learning

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Document pages: 14 pages

Abstract: We propose a graph spectrum-based Gaussian process for prediction of signalsdefined on nodes of the graph. The model is designed to capture various graphsignal structures through a highly adaptive kernel that incorporates a flexiblepolynomial function in the graph spectral domain. Unlike most existingapproaches, we propose to learn such a spectral kernel, where the polynomialsetup enables learning without the need for eigen-decomposition of the graphLaplacian. In addition, this kernel has the interpretability of graph filteringachieved by a bespoke maximum likelihood learning algorithm that enforces thepositivity of the spectrum. We demonstrate the interpretability of the model insynthetic experiments from which we show the various ground truth spectralfilters can be accurately recovered, and the adaptability translates tosuperior performances in the prediction of real-world graph data of variouscharacteristics.

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