Gaussian Processes on Cellular Complexes
Mathieu Alain So Takao Brooks Paige Marc Peter Deisenroth
In recent years, there has been considerable interest in developing machine
learning models on graphs in order to account for topological inductive biases.
In particular, recent attention was given to Gaussian processes on such
structures since they can additionally account for uncertainty. However, graphs
are limited to modelling relations between two vertices. In this paper, we go
beyond this dyadic setting and consider polyadic relations that include
interactions between vertices, edges and one of their generalisations, known as
cells. Specifically, we propose Gaussian processes on cellular complexes, a
generalisation of graphs that captures interactions between these higher-order
cells. One of our key contributions is the derivation of two novel kernels, one
that generalises the graph Mat\'ern kernel and one that additionally mixes
information of different cell types.