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Elementos da teoria de aprendizagem de m\'aquina supervisionada
- Publication Year :
- 2019
-
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.<br />Comment: 390 pp. + vii, in Portuguese, a preliminary version, to be published by IMPA as a book of lectures of the 23nd Brazilian Math Colloquium (July 28 - Aug 2, 2019), submitted to arXiv upon IMPA permission
- Subjects :
- Computer Science - Machine Learning
68Q32, 62H30, 68T05, 68T10
Subjects
Details
- Language :
- Portuguese
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1910.06820
- Document Type :
- Working Paper