Lipschitz extensions in machine learning models: applications to data-driven predictive football
- Autores: Andrés Roger Arnau Notari
- Directores de la Tesis: Enrique Alfonso Sánchez Pérez (dir. tes.), José Manuel Calabuig Rodríguez (dir. tes.)
- Lectura: En la Universitat Politècnica de València ( España ) en 2025
- Idioma: inglés
- Tribunal Calificador de la Tesis: Pablo Gregori Huerta (presid.), Lucía Agud Albesa (secret.), Fernando Galaz-Garcia (voc.)
- Programa de doctorado: Programa de Doctorado en Matemáticas por la Universitat de València (Estudi General) y la Universitat Politècnica de València
- Materias:
- Enlaces
- Tesis en acceso abierto en: RiuNet
- Resumen
This dissertation concerns the theory and application of Lipschitz extensions, focused and applied to predictive and analytical modeling in Machine Learning and football analytics.
The work is divided into two parts.
The first part deals with the mathematical development of extending Lipschitz functions and operators by introducing new methods and generalizations.
The second part applies these techniques to real-world problems in football, demonstrating their practical relevance.
In the theoretical part of the dissertation, the concept of lattice Lipschitz operators particularizes classical Lipschitz continuity to ordered spaces. Explicit extension formulas are derived explicitly, in particular an $p$-average-slope-minimizing extension for $p=2$: smoothness and stability features are investigated.
New solutions are proposed for the problem of extension of lattice Lipschitz operators on finitely dimensional spaces, with a particular emphasis on diagonal representations and reconstructions from sparse data.
In the applied part, two big problems are investigated.
First, a model is proposed to predict the future market value of football players based on player statistics and performance metrics.
The model, based on Lipschitz-type extension formulas, offer a more interpretable approach than other common models.
An offline Reinforcement Learning framework (where the agent does not interact directly with the environmentz) for offensive analysis of football is also used for deriving optimal strategies for gameplay.
These contributions are of both theoretical and practical value.
From the theoretical point of view, this dissertation contributes to functional analysis, developing new tools for the study and extension of Lipschitz functions and introducing a new class of operators to be examined.
On the more practical side, it bridges abstract mathematics with sports analytics, offering innovative solutions for player valuation and tactical analysis in football.
