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.

在线预测中的回合切换是文献中广泛研究的一个问题，INTEL 算法运用高斯过程的非参数灵活性提供了一种在线预测回合切换时间序列的方法，该方法通过自适应地结合多个候选模型来实现，我们介绍了 LINTEL 算法，它使用了时间 t 的精确滤波分布进行常量更新，使得流式算法的时间复杂度达到了最优，此外，我们还提出了一种基于算术平均的融合策略，以更好地适应 LINTEL 算法的加权机制，实验证明我们的方法在合理的设置下比 INTEL 算法快五倍以上，并且预测质量更好。