# Learning with Hierarchical Gaussian Kernels

arXiv: https://arxiv.org/abs/1612.00824 · HTML: https://mlsanity.com/paper/1612.00824/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2016.

## Built on by (most cited first, 4 of 4)

- [Bayesian Optimization over Hybrid Spaces](https://mlsanity.com/paper/2106.04682/) (2021)
- [Analysis of Structured Deep Kernel Networks](https://mlsanity.com/paper/2105.07228/) (2021)
- [Learning Analysis of Kernel Ridgeless Regression with Asymmetric Kernel Learning](https://mlsanity.com/paper/2406.01435/) (2024)
- [Enhancing Kernel Flexibility via Learning Asymmetric Locally-Adaptive Kernels](https://mlsanity.com/paper/2310.05236/) (2023)

## Abstract (arXiv)

We investigate iterated compositions of weighted sums of Gaussian kernels and provide an interpretation of the construction that shows some similarities with the architectures of deep neural networks. On the theoretical side, we show that these kernels are universal and that SVMs using these kernels are universally consistent. We further describe a parameter optimization method for the kernel parameters and empirically compare this method to SVMs, random forests, a multiple kernel learning approach, and to some deep neural networks.