Improving Generalisation in Multi-Output Gaussian Processes for Time Series Prediction

Felix Opolka, Wessel Bruinsma, Yuting Wu, Pietro Lio, Eric Perim

Keywords: spatio-temporal graphs, Gaussian processes, time series

Abstract:

Multi-output time series, and spatio-temporal graphs in particular, are powerful modelling tools for a variety of real-world scenarios.
Gaussian processes linear mixing models are a common way to address these tasks, modelling both correlations in time and between time series by correlating a small number of latent processes using a mixing matrix.
However, existing methods can suffer from overfitting and are difficult to combine with additional graph structure information in case of spatio-temporal graphs.
In this short paper, we propose a novel, more parameter-efficient parameterisation of the mixing matrix by representing processes by states in a latent space and deriving correlations between processes from their relative positions.
This formulation allows us to incorporate adjacency information between the time series by placing a prior on the process states and smoothing them using a low-pass graph filter.
We show that our approach improves on existing GP mixing models on two traffic forecasting data sets by reducing overfitting and improving inductive bias