# Streaming Sparse Gaussian Process Approximations

arXiv: https://arxiv.org/abs/1705.07131 · HTML: https://mlsanity.com/paper/1705.07131/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2017.

## Built on by (most cited first, 30 of 41)

- [Information-theoretic Online Memory Selection for Continual Learning](https://mlsanity.com/paper/2204.04763/) (2022)
- [Continual Learning via Sequential Function-Space Variational Inference](https://mlsanity.com/paper/2312.17210/) (2023)
- [Conditioning Sparse Variational Gaussian Processes for Online Decision-making](https://mlsanity.com/paper/2110.15172/) (2021)
- [Kernel Interpolation for Scalable Online Gaussian Processes](https://mlsanity.com/paper/2103.01454/) (2021)
- [Incremental Ensemble Gaussian Processes](https://mlsanity.com/paper/2110.06777/) (2021)
- [Partitioned Variational Inference: A Framework for Probabilistic Federated Learning](https://mlsanity.com/paper/2202.12275/) (2022)
- [Memory-Based Dual Gaussian Processes for Sequential Learning](https://mlsanity.com/paper/2306.03566/) (2023)
- [Adaptive Inducing Points Selection For Gaussian Processes](https://mlsanity.com/paper/2107.10066/) (2021)
- [Correlated Product of Experts for Sparse Gaussian Process Regression](https://mlsanity.com/paper/2112.09519/) (2021)
- [Fantasizing with Dual GPs in Bayesian Optimization and Active Learning](https://mlsanity.com/paper/2211.01053/) (2022)
- [Knowledge Adaptation as Posterior Correction](https://mlsanity.com/paper/2506.14262/) (2025)
- [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)
- [Data-driven Science and Machine Learning Methods in Laser-Plasma Physics](https://mlsanity.com/paper/2212.00026/) (2022)
- [Fully Bayesian Differential Gaussian Processes through Stochastic Differential Equations](https://mlsanity.com/paper/2408.06069/) (2024)
- [Streaming Bayes GFlowNets](https://mlsanity.com/paper/2411.05899/) (2024)
- [Adaptive Sparse Gaussian Process](https://mlsanity.com/paper/2302.10325/) (2023)
- [Active Cost-aware Labeling of Streaming Data](https://mlsanity.com/paper/2304.06808/) (2023)
- [Networked Online Learning for Control of Safety-Critical Resource-Constrained Systems based on Gaussian Processes](https://mlsanity.com/paper/2202.11491/) (2022)
- [Recurrent Memory for Online Interdomain Gaussian Processes](https://mlsanity.com/paper/2502.08736/) (2025)
- [Robust, Online, and Adaptive Decentralized Gaussian Processes](https://mlsanity.com/paper/2509.18011/) (2025)
- [Incremental Transformer Neural Processes](https://mlsanity.com/paper/2602.18955/) (2026)
- [Active and sparse methods in smoothed model checking](https://mlsanity.com/paper/2104.09940/) (2021)
- [Modular Gaussian Processes for Transfer Learning](https://mlsanity.com/paper/2110.13515/) (2021)
- [Volatility Based Kernels and Moving Average Means for Accurate Forecasting with Gaussian Processes](https://mlsanity.com/paper/2207.06544/) (2022)
- [Beyond Intuition, a Framework for Applying GPs to Real-World Data](https://mlsanity.com/paper/2307.03093/) (2023)
- [Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Models](https://mlsanity.com/paper/2402.18946/) (2024)
- [Adjusting Model Size in Continual Gaussian Processes: How Big is Big Enough?](https://mlsanity.com/paper/2408.07588/) (2024)
- [Likelihood approximations via Gaussian approximate inference](https://mlsanity.com/paper/2410.20754/) (2024)

## Abstract (arXiv)

Sparse pseudo-point approximations for Gaussian process (GP) models provide a suite of methods that support deployment of GPs in the large data regime and enable analytic intractabilities to be sidestepped. However, the field lacks a principled method to handle streaming data in which both the posterior distribution over function values and the hyperparameter estimates are updated in an online fashion. The small number of existing approaches either use suboptimal hand-crafted heuristics for hyperparameter learning, or suffer from catastrophic forgetting or slow updating when new data arrive. This paper develops a new principled framework for deploying Gaussian process probabilistic models in the streaming setting, providing methods for learning hyperparameters and optimising pseudo-input locations. The proposed framework is assessed using synthetic and real-world datasets.