# Adaptive Sparse Gaussian Process

arXiv: https://arxiv.org/abs/2302.10325 · HTML: https://mlsanity.com/paper/2302.10325/

## Key facts

- Cited by 3 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 20 Feb 2023.

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

- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Streaming Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1705.07131/) (2017)
- [Kernel Interpolation for Scalable Online Gaussian Processes](https://mlsanity.com/paper/2103.01454/) (2021)
- [Consistent Online Gaussian Process Regression Without the Sample Complexity Bottleneck](https://mlsanity.com/paper/2004.11094/) (2020)
- [Scalable Gaussian Processes with Grid-Structured Eigenfunctions (GP-GRIEF)](https://mlsanity.com/paper/1807.02125/) (2018)
- [Real-Time Regression with Dividing Local Gaussian Processes](https://mlsanity.com/paper/2006.09446/) (2020)

## Built on by (most cited first, 3 of 3)

- [Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Models](https://mlsanity.com/paper/2402.18946/) (2024)
- [Streaming Bayesian Modeling for predicting Fat-Tailed Customer Lifetime Value](https://mlsanity.com/paper/2312.00373/) (2023)
- [Learning Context-conditioned Gaussian Overbounds for Convolution-Based Uncertainty Propagation](https://mlsanity.com/paper/2605.15789/) (2026)

## Abstract (arXiv)

Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data and with the lowest possible computational cost for online parameter updating. Existing solutions only partially cover these needs. Here, we propose the first adaptive sparse Gaussian Process (GP) able to address all these issues. We first reformulate a variational sparse GP algorithm to make it adaptive through a forgetting factor. Next, to make the model inference as simple as possible, we propose updating a single inducing point of the sparse GP model together with the remaining model parameters every time a new sample arrives. As a result, the algorithm presents a fast convergence of the inference process, which allows an efficient model update (with a single inference iteration) even in highly non-stationary environments. Experimental results demonstrate the capabilities of the proposed algorithm and its good performance in modeling the predictive posterior in mean and confidence interval estimation compared to state-of-the-art approaches.