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

arXiv: https://arxiv.org/abs/2406.00570 · HTML: https://mlsanity.com/paper/2406.00570/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 1 Jun 2024.

## Builds on (most cited first, 9 of 9)

- [Generalized Product of Experts for Automatic and Principled Fusion of Gaussian Process Predictions](https://mlsanity.com/paper/1410.7827/) (2014)
- [Incremental Ensemble Gaussian Processes](https://mlsanity.com/paper/2110.06777/) (2021)
- [Combining probability distributions: Extending the logarithmic pooling approach](https://mlsanity.com/paper/1502.04206/) (2015)
- [Sequential online prediction in the presence of outliers and change points: an instant temporal structure learning approach](https://mlsanity.com/paper/1907.06377/) (2019)
- [Hida-Mat'ern Kernel](https://mlsanity.com/paper/2107.07098/) (2021)
- [Online Time Series Anomaly Detection with State Space Gaussian Processes](https://mlsanity.com/paper/2201.06763/) (2022)
- [Dynamic Online Ensembles of Basis Expansions](https://mlsanity.com/paper/2405.01365/) (2024)
- [Second Order Statistics Analysis and Comparison between Arithmetic and Geometric Average Fusion](https://mlsanity.com/paper/1901.08015/) (2019)
- [Robust Sequential Online Prediction with Dynamic Ensemble of Multiple Models: A Review](https://mlsanity.com/paper/2112.02374/) (2021)

## Built on by (most cited first, 2 of 2)

- [Robust and Conjugate Spatio-Temporal Gaussian Processes](https://mlsanity.com/paper/2502.02450/) (2025)
- [Robust, Online, and Adaptive Decentralized Gaussian Processes](https://mlsanity.com/paper/2509.18011/) (2025)

## Abstract (arXiv)

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.