Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets
This work addresses the need for multi-scale graph models in machine learning, offering an incremental improvement with adaptive wavelets for better data representation.
The paper tackles the problem of modeling data with varying smoothness on graphs by proposing a Gaussian process model using spectral graph wavelets, which automatically adapts to different frequencies through hyperparameter optimization and achieves competitive performance in graph-based learning tasks.
Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the relevant information. In this work, we propose a Gaussian process model using spectral graph wavelets, which can naturally aggregate neighbourhood information at different scales. Through maximum likelihood optimisation of the model hyperparameters, the wavelets automatically adapt to the different frequencies in the data, and as a result our model goes beyond capturing low frequency information. We achieve scalability to larger graphs by using a spectrum-adaptive polynomial approximation of the filter function, which is designed to yield a low approximation error in dense areas of the graph spectrum. Synthetic and real-world experiments demonstrate the ability of our model to infer scales accurately and produce competitive performances against state-of-the-art models in graph-based learning tasks.