# Deep Gaussian Processes with Convolutional Kernels

arXiv: https://arxiv.org/abs/1806.01655 · HTML: https://mlsanity.com/paper/1806.01655/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2018.

## Built on by (most cited first, 7 of 7)

- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processes](https://mlsanity.com/paper/2309.12658/) (2023)
- [Distributional Gaussian Processes Layers for Out-of-Distribution Detection](https://mlsanity.com/paper/2206.13346/) (2022)
- [A Multitask Deep Learning Model for Classification and Regression of Hyperspectral Images: Application to the large-scale dataset](https://mlsanity.com/paper/2407.16384/) (2024)
- [Ischemic Stroke Lesion Prediction using imbalanced Temporal Deep Gaussian Process (iTDGP)](https://mlsanity.com/paper/2211.09068/) (2022)
- [Gaussian Process Model with Tensorial Inputs and Its Application to the Design of 3D Printed Antennas](https://mlsanity.com/paper/2407.15877/) (2024)
- [Scalable Gaussian process inference via neural feature maps](https://mlsanity.com/paper/2605.10285/) (2026)

## Abstract (arXiv)

Deep Gaussian processes (DGPs) provide a Bayesian non-parametric alternative to standard parametric deep learning models. A DGP is formed by stacking multiple GPs resulting in a well-regularized composition of functions. The Bayesian framework that equips the model with attractive properties, such as implicit capacity control and predictive uncertainty, makes it at the same time challenging to combine with a convolutional structure. This has hindered the application of DGPs in computer vision tasks, an area where deep parametric models (i.e. CNNs) have made breakthroughs. Standard kernels used in DGPs such as radial basis functions (RBFs) are insufficient for handling pixel variability in raw images. In this paper, we build on the recent convolutional GP to develop Convolutional DGP (CDGP) models which effectively capture image level features through the use of convolution kernels, therefore opening up the way for applying DGPs to computer vision tasks. Our model learns local spatial influence and outperforms strong GP based baselines on multi-class image classification. We also consider various constructions of convolution kernel over the image patches, analyze the computational trade-offs and provide an efficient framework for convolutional DGP models. The experimental results on image data such as MNIST, rectangles-image, CIFAR10 and Caltech101 demonstrate the effectiveness of the proposed approaches.