Probabilistic morphisms and Bayesian supervised learning

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.

v.3: typos corrected, Example 4.11 expanded, 21 p., published in Math. Sbornik, 216 (2025), Nr. 5