Elementos da teoria de aprendizagem de m\'aquina supervisionada

TL;DR

This paper provides comprehensive lecture notes on foundational concepts of supervised machine learning, covering topics from geometry and measure concentration to VC dimension and universal approximation, suitable for advanced students.

Contribution

It offers a self-contained, detailed introduction to key theoretical aspects of supervised learning, including proofs and mathematical background in Portuguese.

Findings

Explains the geometry of the Hamming cube and measure concentration.

Details VC dimension, PAC learnability, and universal consistency.

Includes mathematical foundations with appendices on metric and measure theory.

Abstract

This is a set of lecture notes for an introductory course (advanced undergaduates or the 1st graduate course) on foundations of supervised machine learning (in Portuguese). The topics include: the geometry of the Hamming cube, concentration of measure, shattering and VC dimension, Glivenko-Cantelli classes, PAC learnability, universal consistency and the k-NN classifier in metric spaces, dimensionality reduction, universal approximation, sample compression. There are appendices on metric and normed spaces, measure theory, etc., making the notes self-contained. Este \'e um conjunto de notas de aula para um curso introdut\'orio (curso de gradua\c{c}\~ao avan\c{c}ado ou o 1o curso de p\'os) sobre fundamentos da aprendizagem de m\'aquina supervisionada (em Portugu\^es). Os t\'opicos incluem: a geometria do cubo de Hamming, concentra\c{c}\~ao de medida, fragmenta\c{c}\~ao e dimens\~ao de Vapnik-Chervonenkis, classes de Glivenko-Cantelli, aprendizabilidade PAC, consist\^encia universal e o classificador k-NN em espa\c{c}os m\'etricos, redu\c{c}\~ao de dimensionalidade, aproxima\c{c}\~ao universal, compress\~ao amostral. H\'a ap\^endices sobre espa\c{c}os m\'etricos e normados, teoria de medida, etc., tornando as notas autosuficientes.