A Gaussian Process-based Streaming Algorithm for Prediction of Time Series With Regimes and Outliers

Online prediction of time series under regime switching is a widely studied problem in the literature, with many celebrated approaches. Using the non-parametric flexibility of Gaussian processes, the recently proposed INTEL algorithm provides a product of experts approach to online prediction of time series under possible regime switching, including the special case of outliers. This is achieved by adaptively combining several candidate models, each reporting their predictive distribution at time $t$. However, the INTEL algorithm uses a finite context window approximation to the predictive distribution, the computation of which scales cubically with the maximum lag, or otherwise scales quartically with exact predictive distributions. We introduce LINTEL, which uses the exact filtering distribution at time $t$ with constant-time updates, making the time complexity of the streaming algorithm optimal. We additionally note that the weighting mechanism of INTEL is better suited to a mixture of experts approach, and propose a fusion policy based on arithmetic averaging for LINTEL. We show experimentally that our proposed approach is over five times faster than INTEL under reasonable settings with better quality predictions.