# A Kernel for Hierarchical Parameter Spaces

arXiv: https://arxiv.org/abs/1310.5738 · HTML: https://mlsanity.com/paper/1310.5738/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2013.

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

- [HPOBench: A Collection of Reproducible Multi-Fidelity Benchmark Problems for HPO](https://mlsanity.com/paper/2109.06716/) (2021)
- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [A distance for mixed-variable and hierarchical domains with meta variables](https://mlsanity.com/paper/2405.13073/) (2024)
- [Modeling Hierarchical Spaces: A Review and Unified Framework for Surrogate-Based Architecture Design](https://mlsanity.com/paper/2506.22621/) (2025)

## Abstract (arXiv)

We define a family of kernels for mixed continuous/discrete hierarchical parameter spaces and show that they are positive definite.