Space optimization of functions for machine learning: An approach with Hilbert spaces

In this seminar, the main machine learning problems were addressed as optimization problems in vector spaces of functions, with an emphasis on Hilbert spaces. We discuss the fundamental concepts of these spaces, such as inner products, orthogonality, and projection, and examine how these principles underlie optimization methods in infinite-dimensional spaces. The practical application of these concepts was illustrated through data analysis examples, making their relevance in the context of machine learning clearer.