Supervised learning with probabilistic morphisms and kernel mean embeddings
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908340690354176 |
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| author | Lê, Hông Vân |
| author_facet | Lê, Hông Vân |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06348 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Supervised learning with probabilistic morphisms and kernel mean embeddings Lê, Hông Vân Statistics Theory Machine Learning Category Theory Functional Analysis Probability 46N30, 60B10, 62G05, 18N99 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. |
| title | Supervised learning with probabilistic morphisms and kernel mean embeddings |
| topic | Statistics Theory Machine Learning Category Theory Functional Analysis Probability 46N30, 60B10, 62G05, 18N99 |
| url | https://arxiv.org/abs/2305.06348 |