# On power sum kernels on symmetric groups

arXiv: https://arxiv.org/abs/2211.05650 · HTML: https://mlsanity.com/paper/2211.05650/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 23 references that are in the map.
- First posted on arXiv 10 Nov 2022.

## Builds on (most cited first, 4 of 4)

- [Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact case](https://mlsanity.com/paper/2208.14960/) (2022)
- [Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernels](https://mlsanity.com/paper/2111.01460/) (2021)
- [Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernels](https://mlsanity.com/paper/2110.14423/) (2021)
- [Gaussian Process Manifold Interpolation for Probabilistic Atrial Activation Maps and Uncertain Conduction Velocity](https://mlsanity.com/paper/2004.10586/) (2020)

## Abstract (arXiv)

In this note, we introduce a family of "power sum" kernels and the corresponding Gaussian processes on symmetric groups Sn. Such processes are bi-invariant: the action of Sn on itself from both sides does not change their finite-dimensional distributions. We show that the values of power sum kernels can be efficiently calculated, and we also propose a method enabling approximate sampling of the corresponding Gaussian processes with polynomial computational complexity. By doing this we provide the tools that are required to use the introduced family of kernels and the respective processes for statistical modeling and machine learning.