Gaussian Processes Over Graphs
This work addresses the challenge of improving prediction accuracy for graph-based signals in domains like sensor networks or social networks, though it is incremental as it builds on existing Gaussian process methods by adding graph regularization.
The authors tackled the problem of predicting signals over graphs by proposing Gaussian processes over graphs (GPG), which incorporate graph structure via Laplacian-based regularization to enforce specific spectral profiles like lowpass or bandpass signals. They proved that GPG reduces predictive variance compared to conventional Gaussian processes for any non-trivial graph and demonstrated superior performance in experiments with small or noisy training data.
We propose Gaussian processes for signals over graphs (GPG) using the apriori knowledge that the target vectors lie over a graph. We incorporate this information using a graph- Laplacian based regularization which enforces the target vectors to have a specific profile in terms of graph Fourier transform coeffcients, for example lowpass or bandpass graph signals. We discuss how the regularization affects the mean and the variance in the prediction output. In particular, we prove that the predictive variance of the GPG is strictly smaller than the conventional Gaussian process (GP) for any non-trivial graph. We validate our concepts by application to various real-world graph signals. Our experiments show that the performance of the GPG is superior to GP for small training data sizes and under noisy training.