August 11, 2025Sbornik Mathematics

Probabilistic morphisms and Bayesian supervised learning

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Bayesian supervised learning is unified through probabilistic morphisms, enhancing existing models with fresh insights.
A novel framework emphasizes the role of Markov kernels in Bayesian inversions, facilitating a deeper understanding of density estimation.
Gaussian process regressions are illustrated as practical applications within the developed model, highlighting versatility.
This approach suggests implications for future research into categorical methods in probabilistic modeling, warranting further exploration.

Implication

This framework demonstrates Bayesian density estimation in supervised learning, suggesting new insights into Markov kernels.

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.

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Hông Vân Lê (2025) studied this question.

synapsesocial.com/papers/68a35eeb0a429f7973327d4f https://doi.org/10.4213/sm10191e

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Implication

This framework demonstrates Bayesian density estimation in supervised learning, suggesting new insights into Markov kernels.

Probabilistic morphisms and Bayesian supervised learning

Key Points

Implication

Abstract

Discussion

Cite This Study

Probabilistic morphisms and Bayesian supervised learning

Key Points

Implication

Abstract

Discussion

Cite This Study

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