Título: Variational problems on ransom structures: analysis and applications to machine learning
Abstract: Modern data-acquisition technology produces a wealth of data about the world we live in. The goal of machine learning is to extract and interpret the information the data sets contain. This leads to variety of learning tasks, many of which seek to optimize a functional, defined on the available random sample.
The functionals take as the input the available data samples, yet we seek to make conclusions about the true distribution of data. To compare the outcomes based on finite data and the ideal outcomes that one would have if full information is available, we study the asymptotic properties of the discrete optimization problems based on finite random samples. We will discuss how calculus of variations and partial differential equations provide tools to compare the discrete and continuum descriptions for many relevant problems.
Furthermore, we will discuss how the insights from calculus of variations can be used to guide the design of the functionals used in machine learning.
Location Lunes, 31 de enero de 2022, 14:30-15:30h (horario diferente al habitual!!!!)