Probabilistic morphisms and Bayesian supervised learning

TL;DR

This paper develops a category-theoretic framework for Bayesian supervised learning, including density estimation, and demonstrates its application through Gaussian process regression.

Contribution

It introduces a unified categorical model for Bayesian learning and density estimation using Markov kernels, advancing the theoretical understanding of Bayesian methods.

Findings

Unified categorical framework for Bayesian learning

Application to Gaussian process regression

Enhanced understanding of Bayesian density estimation

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.