Probabilidade em alta dimensão com aplicações em ciência de dados

Abstract

With the advancement of machine learning, new challenges have arisen in the creation and analysis of efficient predictive algorithms. One of the main obstacles is the curse of dimensionality, in which the increase in the number of variables compromises the performance of usual models. This loss of predictive power arises from the behavior of random variables in high dimensions, a phenomenon that can be explained through results from probability and statistical learning theory. In this work, we present and demonstrate these foundations, highlighting the central role of measure concentration in their deductions. To make understanding more intuitive, we perform simulations that illustrate these concepts. Finally, we discuss how this theory can support methods capable of mitigating the challenges imposed by high dimensionality.