Practical Non-Stationary Graph Gaussian Processes

K. S. Sesh Kumar, Viacheslav Borovitskiy

Gaussian processes on graphs provide a principled framework for prediction and uncertainty estimation, but modelling heterogeneous networks often requires balancing flexibility against parameter complexity. Variability at a node may reflect useful signal that should propagate through the network, unreliable measurements whose influence should be suppressed, or a mixture of both. We introduce Variance-Coupled Gaussian Processes (VCGPs), which use a positive auxiliary signal to modulate graph interactions through a single learned coupling exponent. The exponent controls how strongly high-variability nodes propagate or attenuate information, while a cluster-wise extension accommodates different regimes within the same graph. Under stated structural assumptions, we characterize the unique stationary-rescaling point of the basic family, where correlations match those of a stationary graph kernel while node-dependent variances remain. Experiments on traffic, air-quality and weather datasets show competitive prediction and uncertainty estimation relative to stationary and per-node non-stationary baselines, with the largest gains on networks requiring multiple coupling regimes.…