Probabilistic morphisms and Bayesian supervised learning
Statistics Theory
2025-07-08 v3 Category Theory
Statistics Theory
Abstract
In this paper, we develop category theory of Markov kernels to study categorical aspects of Bayesian inversions. As a result, we present a unified model for Bayesian supervised learning, encompassing Bayesian density estimation. We illustrate this model with Gaussian process regressions.
Cite
@article{arxiv.2502.15408,
title = {Probabilistic morphisms and Bayesian supervised learning},
author = {Hông Vân Lê},
journal= {arXiv preprint arXiv:2502.15408},
year = {2025}
}
Comments
v.3: typos corrected, Example 4.11 expanded, 21 p., published in Math. Sbornik, 216 (2025), Nr. 5