  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.
