A Gaussian Process-based Streaming Algorithm for Prediction of Time Series With Regimes and Outliers
This work addresses the computational inefficiency in time series prediction for applications requiring real-time processing, though it is incremental as it builds on the INTEL algorithm with improvements in speed and accuracy.
The authors tackled the problem of online prediction for time series with regime switching and outliers by introducing LINTEL, a Gaussian process-based streaming algorithm that uses exact filtering distributions for constant-time updates, resulting in over five times faster performance and better prediction quality compared to the existing INTEL algorithm.
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.