Upper bounds on the Natarajan dimensions of some function classes

The Natarajan dimension is a fundamental tool for characterizing multi-class PAC learnability, generalizing the Vapnik-Chervonenkis (VC) dimension from binary to multi-class classification problems. This work establishes upper bounds on Natarajan dimensions for certain function classes, including (i...

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Bibliographic Details
Main Author Jin, Ying
Format Journal Article
LanguageEnglish
Published 14.09.2022
Subjects
Computer Science - Learning
Statistics - Machine Learning
Online AccessGet full text
DOI10.48550/arxiv.2209.07015

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Summary:The Natarajan dimension is a fundamental tool for characterizing multi-class PAC learnability, generalizing the Vapnik-Chervonenkis (VC) dimension from binary to multi-class classification problems. This work establishes upper bounds on Natarajan dimensions for certain function classes, including (i) multi-class decision tree and random forests, and (ii) multi-class neural networks with binary, linear and ReLU activations. These results may be relevant for describing the performance of certain multi-class learning algorithms.
DOI:10.48550/arxiv.2209.07015