# Variational Gaussian Processes: A Functional Analysis View

arXiv: https://arxiv.org/abs/2110.12798 · HTML: https://mlsanity.com/paper/2110.12798/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 25 Oct 2021.

## Builds on (most cited first, 14 of 14)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [Less is More: Nystr"om Computational Regularization](https://mlsanity.com/paper/1507.04717/) (2015)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [On Sparse variational methods and the Kullback-Leibler divergence between stochastic processes](https://mlsanity.com/paper/1504.07027/) (2015)
- [Sparse Gaussian Processes with Spherical Harmonic Features](https://mlsanity.com/paper/2006.16649/) (2020)
- [A Tutorial on Sparse Gaussian Processes and Variational Inference](https://mlsanity.com/paper/2012.13962/) (2020)
- [SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data](https://mlsanity.com/paper/2105.04211/) (2021)
- [Variational Inference for Gaussian Process Models with Linear Complexity](https://mlsanity.com/paper/1711.10127/) (2017)
- [Orthogonally Decoupled Variational Gaussian Processes](https://mlsanity.com/paper/1809.08820/) (2018)
- [Connections and Equivalences between the Nystr"om Method and Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2106.01121/) (2021)
- [Fast DPP Sampling for Nystr"om with Application to Kernel Methods](https://mlsanity.com/paper/1603.06052/) (2016)

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

- [Diffusion Generative Models in Infinite Dimensions](https://mlsanity.com/paper/2212.00886/) (2022)
- [Variational Autoencoding Neural Operators](https://mlsanity.com/paper/2302.10351/) (2023)
- [Generalized Variational Inference in Function Spaces: Gaussian Measures meet Bayesian Deep Learning](https://mlsanity.com/paper/2205.06342/) (2022)

## Abstract (arXiv)

Variational Gaussian process (GP) approximations have become a standard tool in fast GP inference. This technique requires a user to select variational features to increase efficiency. So far the common choices in the literature are disparate and lacking generality. We propose to view the GP as lying in a Banach space which then facilitates a unified perspective. This is used to understand the relationship between existing features and to draw a connection between kernel ridge regression and variational GP approximations.