Supervised learning with probabilistic morphisms and kernel mean embeddings

• URL: http://arxiv.org/abs/2305.06348v5
• Date: Wed, 15 Nov 2023 15:12:42 GMT
• Title: Supervised learning with probabilistic morphisms and kernel mean embeddings
• Authors: H\^ong V\^an L\^e
• Abstract summary: I propose a generative model of supervised learning that unifies two approaches to supervised learning. I address two measurability problems, which have been ignored in statistical learning theory. I present a variant of Vapnik-Stefanuyk's regularization method for solving ill-posed problems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper I propose a generative model of supervised learning that unifies two approaches to supervised learning, using a concept of a correct loss function. Addressing two measurability problems, which have been ignored in statistical learning theory, I propose to use convergence in outer probability to characterize the consistency of a learning algorithm. Building upon these results, I extend a result due to Cucker-Smale, which addresses the learnability of a regression model, to the setting of a conditional probability estimation problem. Additionally, I present a variant of Vapnik-Stefanuyk's regularization method for solving stochastic ill-posed problems, and using it to prove the generalizability of overparameterized supervised learning models.

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