Matérn Gaussian Processes on Graphs
This work addresses a gap in Gaussian process modeling for graph-structured data, making these models more accessible for practitioners in machine learning applications involving graphs.
The authors tackled the problem of limited Gaussian process models for undirected graphs by extending Matérn Gaussian processes from Euclidean to graph settings, showing that the resulting models inherit desirable properties and can be trained with standard methods like inducing points.
Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the input space is Euclidean, the choice is much more limited for Gaussian processes whose input space is an undirected graph. In this work, we leverage the stochastic partial differential equation characterization of Matérn Gaussian processes - a widely-used model class in the Euclidean setting - to study their analog for undirected graphs. We show that the resulting Gaussian processes inherit various attractive properties of their Euclidean and Riemannian analogs and provide techniques that allow them to be trained using standard methods, such as inducing points. This enables graph Matérn Gaussian processes to be employed in mini-batch and non-conjugate settings, thereby making them more accessible to practitioners and easier to deploy within larger learning frameworks.