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
Published inProceedings / IEEE International Symposium on Information Theory pp. 1020 - 1025
Main Author Jin, Ying
Format Conference Proceeding
LanguageEnglish
Published IEEE 25.06.2023
Subjects
Classification algorithms
Decision trees
Information theory
Neural networks
Picture archiving and communication systems
Random forests
Upper bound
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ISSN2157-8117
DOI10.1109/ISIT54713.2023.10206618

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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.
ISSN:2157-8117
DOI:10.1109/ISIT54713.2023.10206618