# Gaussian Processes for Big Data

arXiv: https://arxiv.org/abs/1309.6835 · HTML: https://mlsanity.com/paper/1309.6835/

## Key facts

- Cited by 383 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2013.

## Built on by (most cited first, 30 of 383)

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- [The Bayesian Learning Rule](https://mlsanity.com/paper/2107.04562/) (2021)
- [Local Latent Space Bayesian Optimization over Structured Inputs](https://mlsanity.com/paper/2201.11872/) (2022)
- [Active Preference-Based Gaussian Process Regression for Reward Learning](https://mlsanity.com/paper/2005.02575/) (2020)
- [Variational Bayesian Last Layers](https://mlsanity.com/paper/2404.11599/) (2024)
- [Bayesian Model Selection, the Marginal Likelihood, and Generalization](https://mlsanity.com/paper/2202.11678/) (2022)
- [Bayesian Learning via Neural Schr"odinger-F"ollmer Flows](https://mlsanity.com/paper/2111.10510/) (2021)
- [Optimal Order Simple Regret for Gaussian Process Bandits](https://mlsanity.com/paper/2108.09262/) (2021)
- [GAUCHE: A Library for Gaussian Processes in Chemistry](https://mlsanity.com/paper/2212.04450/) (2022)
- [Spatio-Temporal Variational Gaussian Processes](https://mlsanity.com/paper/2111.01732/) (2021)
- [Inducing Point Allocation for Sparse Gaussian Processes in High-Throughput Bayesian Optimisation](https://mlsanity.com/paper/2301.10123/) (2023)
- [Discovering Many Diverse Solutions with Bayesian Optimization](https://mlsanity.com/paper/2210.10953/) (2022)
- [Sampling from Gaussian Process Posteriors using Stochastic Gradient Descent](https://mlsanity.com/paper/2306.11589/) (2023)
- [Deep Neural Networks as Point Estimates for Deep Gaussian Processes](https://mlsanity.com/paper/2105.04504/) (2021)
- [Sequential Deconfounding for Causal Inference with Unobserved Confounders](https://mlsanity.com/paper/2104.09323/) (2021)
- [Posterior and Computational Uncertainty in Gaussian Processes](https://mlsanity.com/paper/2205.15449/) (2022)
- [Preconditioning for Scalable Gaussian Process Hyperparameter Optimization](https://mlsanity.com/paper/2107.00243/) (2021)
- [Conditioning Sparse Variational Gaussian Processes for Online Decision-making](https://mlsanity.com/paper/2110.15172/) (2021)
- [Generalized Variational Inference in Function Spaces: Gaussian Measures meet Bayesian Deep Learning](https://mlsanity.com/paper/2205.06342/) (2022)
- [Calibrating Transformers via Sparse Gaussian Processes](https://mlsanity.com/paper/2303.02444/) (2023)
- [AutoIP: A United Framework to Integrate Physics into Gaussian Processes](https://mlsanity.com/paper/2202.12316/) (2022)
- [Multi-Fidelity Cost-Aware Bayesian Optimization](https://mlsanity.com/paper/2211.02732/) (2022)
- [Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernels](https://mlsanity.com/paper/2110.14423/) (2021)
- [Dual Parameterization of Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2111.03412/) (2021)
- [Kernel Interpolation for Scalable Online Gaussian Processes](https://mlsanity.com/paper/2103.01454/) (2021)
- [BOiLS: Bayesian Optimisation for Logic Synthesis](https://mlsanity.com/paper/2111.06178/) (2021)
- [Theoretical characterization of uncertainty in high-dimensional linear classification](https://mlsanity.com/paper/2202.03295/) (2022)
- [Improved Convergence Rates for Sparse Approximation Methods in Kernel-Based Learning](https://mlsanity.com/paper/2202.04005/) (2022)
- [Sampling-based inference for large linear models, with application to linearised Laplace](https://mlsanity.com/paper/2210.04994/) (2022)

## Abstract (arXiv)

We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to depend on a set of globally relevant inducing variables which factorize the model in the necessary manner to perform variational inference. Our ap- proach is readily extended to models with non-Gaussian likelihoods and latent variable models based around Gaussian processes. We demonstrate the approach on a simple toy problem and two real world data sets.