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math.ST2026

Estimating conditional expectation

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In this paper, we consider the problem of estimating conditional expectations as an ill-posed inverse problem. We propose a solution based on a generalization of Vapnik's theorem \…

math.ST2026

Batch learning equals online learning in Bayesian supervised learning

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In this paper we study Bayesian supervised learning models proposed by Lê in \cite{Le2025}. Using functoriality of probabilistic morphisms, we prove that sequential and batch Baye…

math.ST2025

Probabilistic morphisms and Bayesian supervised learning

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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 lea…