# Categorical and geometric methods in statistical, manifold, and machine learning

arXiv: https://arxiv.org/abs/2505.03862 · HTML: https://mlsanity.com/paper/2505.03862/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 66 references that are in the map.
- First posted on arXiv 6 May 2025.

## Builds on (most cited first, 5 of 5)

- [The Modern Mathematics of Deep Learning](https://mlsanity.com/paper/2105.04026/) (2021)
- [A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics](https://mlsanity.com/paper/1908.07021/) (2019)
- [Geodesic Exponential Kernels: When Curvature and Linearity Conflict](https://mlsanity.com/paper/1411.0296/) (2014)
- [Kernel Methods on Riemannian Manifolds with Gaussian RBF Kernels](https://mlsanity.com/paper/1412.0265/) (2014)
- [Supervised learning with probabilistic morphisms and kernel mean embeddings](https://mlsanity.com/paper/2305.06348/) (2023)

## Abstract (arXiv)

We present and discuss applications of the category of probabilistic morphisms, initially developed in citeLe2023, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall be, along with many other topics, considered in depth in the forthcoming book citeLMPT2024.