# Infinite-Horizon Gaussian Processes

arXiv: https://arxiv.org/abs/1811.06588 · HTML: https://mlsanity.com/paper/1811.06588/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2018.

## Built on by (most cited first, 6 of 6)

- [Knowledge-Adaptation Priors](https://mlsanity.com/paper/2106.08769/) (2021)
- [Sparse Algorithms for Markovian Gaussian Processes](https://mlsanity.com/paper/2103.10710/) (2021)
- [Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processes](https://mlsanity.com/paper/2106.10210/) (2021)
- [Hida-Mat'ern Kernel](https://mlsanity.com/paper/2107.07098/) (2021)
- [Linear Time GPs for Inferring Latent Trajectories from Neural Spike Trains](https://mlsanity.com/paper/2306.01802/) (2023)
- [Motion Prediction with Gaussian Processes for Safe Human-Robot Interaction in Virtual Environments](https://mlsanity.com/paper/2405.09109/) (2024)

## Abstract (arXiv)

Gaussian processes provide a flexible framework for forecasting, removing noise, and interpreting long temporal datasets. State space modelling (Kalman filtering) enables these non-parametric models to be deployed on long datasets by reducing the complexity to linear in the number of data points. The complexity is still cubic in the state dimension m which is an impediment to practical application. In certain special cases (Gaussian likelihood, regular spacing) the GP posterior will reach a steady posterior state when the data are very long. We leverage this and formulate an inference scheme for GPs with general likelihoods, where inference is based on single-sweep EP (assumed density filtering). The infinite-horizon model tackles the cubic cost in the state dimensionality and reduces the cost in the state dimension m to O(m2) per data point. The model is extended to online-learning of hyperparameters. We show examples for large finite-length modelling problems, and present how the method runs in real-time on a smartphone on a continuous data stream updated at 100~Hz.