# Convolutional Gaussian Processes

arXiv: https://arxiv.org/abs/1709.01894 · HTML: https://mlsanity.com/paper/1709.01894/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2017.

## Built on by (most cited first, 30 of 44)

- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [The Promises and Pitfalls of Deep Kernel Learning](https://mlsanity.com/paper/2102.12108/) (2021)
- [Pre-trained Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2109.08215/) (2021)
- [Deep Neural Networks as Point Estimates for Deep Gaussian Processes](https://mlsanity.com/paper/2105.04504/) (2021)
- [Sample-Then-Optimize Batch Neural Thompson Sampling](https://mlsanity.com/paper/2210.06850/) (2022)
- [Generalized Variational Inference in Function Spaces: Gaussian Measures meet Bayesian Deep Learning](https://mlsanity.com/paper/2205.06342/) (2022)
- [Combining Multi-Fidelity Modelling and Asynchronous Batch Bayesian Optimization](https://mlsanity.com/paper/2211.06149/) (2022)
- [Deep Learning for Bayesian Optimization of Scientific Problems with High-Dimensional Structure](https://mlsanity.com/paper/2104.11667/) (2021)
- [A spectrum of physics-informed Gaussian processes for regression in engineering](https://mlsanity.com/paper/2309.10656/) (2023)
- [GPflux: A Library for Deep Gaussian Processes](https://mlsanity.com/paper/2104.05674/) (2021)
- [Globally Gated Deep Linear Networks](https://mlsanity.com/paper/2210.17449/) (2022)
- [Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition](https://mlsanity.com/paper/2106.05992/) (2021)
- [Efficient Transformed Gaussian Processes for Non-Stationary Dependent Multi-class Classification](https://mlsanity.com/paper/2205.15008/) (2022)
- [Transferring model structure in Bayesian transfer learning for Gaussian process regression](https://mlsanity.com/paper/2101.06884/) (2021)
- [Learning Interacting Dynamical Systems with Latent Gaussian Process ODEs](https://mlsanity.com/paper/2205.11894/) (2022)
- [Revisiting Active Sets for Gaussian Process Decoders](https://mlsanity.com/paper/2209.04636/) (2022)
- [Sparse Gaussian Process Hyperparameters: Optimize or Integrate?](https://mlsanity.com/paper/2211.02476/) (2022)
- [Actually Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2304.05091/) (2023)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Fully Bayesian Differential Gaussian Processes through Stochastic Differential Equations](https://mlsanity.com/paper/2408.06069/) (2024)
- [Correlated Weights in Infinite Limits of Deep Convolutional Neural Networks](https://mlsanity.com/paper/2101.04097/) (2021)
- [Quasi-Bayesian Nonparametric Density Estimation via Autoregressive Predictive Updates](https://mlsanity.com/paper/2206.06462/) (2022)
- [Convolutional Deep Kernel Machines](https://mlsanity.com/paper/2309.09814/) (2023)
- [Regularized Multi-output Gaussian Convolution Process with Domain Adaptation](https://mlsanity.com/paper/2409.02778/) (2024)
- [Tighter sparse variational Gaussian processes](https://mlsanity.com/paper/2502.04750/) (2025)
- [The Catechol Benchmark: Time-series Solvent Selection Data for Few-shot Machine Learning](https://mlsanity.com/paper/2506.07619/) (2025)
- [Convolutional Normalizing Flows for Deep Gaussian Processes](https://mlsanity.com/paper/2104.08472/) (2021)
- [Unsupervised Restoration of Weather-affected Images using Deep Gaussian Process-based CycleGAN](https://mlsanity.com/paper/2204.10970/) (2022)
- [Incorporating Prior Knowledge into Neural Networks through an Implicit Composite Kernel](https://mlsanity.com/paper/2205.07384/) (2022)
- [Physics-enhanced Gaussian Process Variational Autoencoder](https://mlsanity.com/paper/2305.09006/) (2023)

## Abstract (arXiv)

We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing point approximation that is well-tailored to the convolutional kernel. This allows us to gain the generalisation benefit of a convolutional kernel, together with fast but accurate posterior inference. We investigate several variations of the convolutional kernel, and apply it to MNIST and CIFAR-10, which have both been known to be challenging for Gaussian processes. We also show how the marginal likelihood can be used to find an optimal weighting between convolutional and RBF kernels to further improve performance. We hope that this illustration of the usefulness of a marginal likelihood will help automate discovering architectures in larger models.