# Sequential Gaussian Processes for Online Learning of Nonstationary Functions

arXiv: https://arxiv.org/abs/1905.10003 · HTML: https://mlsanity.com/paper/1905.10003/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2019.

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

- [Joint Link Adaptation and Device Scheduling Approach for URLLC Industrial IoT Network: A DRL-based Method with Bayesian Optimization](https://mlsanity.com/paper/2512.23493/) (2025)
- [Online Student-t Processes with an Overall-local Scale Structure for Modelling Non-stationary Data](https://mlsanity.com/paper/2311.00564/) (2023)

## Abstract (arXiv)

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for modeling real-valued nonlinear functions due to their flexibility and uncertainty quantification. However, the typical GP regression model suffers from several drawbacks: 1) Conventional GP inference scales O(N3) with respect to the number of observations; 2) Updating a GP model sequentially is not trivial; and 3) Covariance kernels typically enforce stationarity constraints on the function, while GPs with non-stationary covariance kernels are often intractable to use in practice. To overcome these issues, we propose a sequential Monte Carlo algorithm to fit infinite mixtures of GPs that capture non-stationary behavior while allowing for online, distributed inference. Our approach empirically improves performance over state-of-the-art methods for online GP estimation in the presence of non-stationarity in time-series data. To demonstrate the utility of our proposed online Gaussian process mixture-of-experts approach in applied settings, we show that we can sucessfully implement an optimization algorithm using online Gaussian process bandits.