Zoran Skoda carenciaBS

• Carl Faith, Rings and things: the fine array of 20th century algebra, AMS
• Popescu, Abelian categories
• Aspinwall et al. Dirichlet branes and mirror symmetry, AMS
• Rowbottom, Frederick and Jonathan Chapman. Relative Category Theory and Geometric Morphisms: A Logical Approach, published in Oxford Logic Guides, Oxford University Press, 1992, ISBN 978-0-19-853434-1
• Jay W. Forrester, Industrial dynamics archive

pers-carencia

• B. Banaschewski, R. Harting, Lattice aspects of radical ideals and choice principles, Proc. London Math. Soc. (1985) s3-50 (3): 385–404 doi

• Kimmo I. Rosenthal, A general approach to Gabriel filters on quantales, Comm. Algebra 20, n.11 (1992) 3393–3409 doi

• James Freitag, Rémi Jaoui, Rahim Moosa, When any three solutions are independent, Invent. math. 230 (2022) 1249–1265 arXiv/2110.08123 doi

• Alberto Canonaco, Mattia Ornaghi, Paolo Stellari, Localizations of the category of A∞ categories and internal Homs over a ring, arXiv:2404.06610

• Leland McInnes, John Healy, James Melville, UMAP: Uniform manifold approximation and projection for dimension deduction, arXiv:1802.03426

• Hông Vân Lê, Supervised learning with probabilistic morphisms and kernel mean embeddings, arXiv:2305.06348

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.