# Temporal Gaussian Process Regression in Logarithmic Time

arXiv: https://arxiv.org/abs/2102.09964 · HTML: https://mlsanity.com/paper/2102.09964/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 19 Feb 2021.

## Builds on (most cited first, 8 of 8)

- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [Generalized Robust Bayesian Committee Machine for Large-scale Gaussian Process Regression](https://mlsanity.com/paper/1806.00720/) (2018)
- [Temporal Parallelization of Bayesian Smoothers](https://mlsanity.com/paper/1905.13002/) (2019)
- [Parallelizable sparse inverse formulation Gaussian processes (SpInGP)](https://mlsanity.com/paper/1610.08035/) (2016)
- [Deep State-Space Gaussian Processes](https://mlsanity.com/paper/2008.04733/) (2020)
- [Embarrassingly Parallel Inference for Gaussian Processes](https://mlsanity.com/paper/1702.08420/) (2017)
- [Parallel Iterated Extended and Sigma-point Kalman Smoothers](https://mlsanity.com/paper/2102.00514/) (2021)

## Built on by (most cited first, 1 of 1)

- [State-space deep Gaussian processes with applications](https://mlsanity.com/paper/2111.12604/) (2021)

## Abstract (arXiv)

The aim of this article is to present a novel parallelization method for temporal Gaussian process (GP) regression problems. The method allows for solving GP regression problems in logarithmic O(log N) time, where N is the number of time steps. Our approach uses the state-space representation of GPs which in its original form allows for linear O(N) time GP regression by leveraging the Kalman filtering and smoothing methods. By using a recently proposed parallelization method for Bayesian filters and smoothers, we are able to reduce the linear computational complexity of the temporal GP regression problems into logarithmic span complexity. This ensures logarithmic time complexity when run on parallel hardware such as a graphics processing unit (GPU). We experimentally demonstrate the computational benefits on simulated and real datasets via our open-source implementation leveraging the GPflow framework.