Probabilistic morphisms and Bayesian supervised learning

H. V. Lê<sup>ab

a</sup> Institute of Mathematics, Czech Academy of Sciences, Praha, Czech Republic
^b Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic

Abstract: We develop the category theory of Markov kernels to the study of categorical aspects of Bayesian inversions. As a result, we present a unified model for Bayesian supervised learning, including Bayesian density estimation. We illustrate this model with Gaussian process regressions.
Bibliography: 20 titles.

Keywords: Markov kernel, Bayesian inversion, category of probabilistic morphisms, Bayesian supervised learning model, Gaussian process regression.

MSC: Primary 62C10; Secondary 62G05, 62G08

Received: 11.09.2024 and 07.02.2025

DOI: 10.4213/sm10191

 English version: Sbornik: Mathematics, 2025, 216:5, 723–741

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