Upper bounds on the Natarajan dimensions of some function classes

Ying Jin

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arXiv · 2209.07015

Upper bounds on the Natarajan dimensions of some function classes

Ying Jin

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Abstract

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.

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Ying Jin. 2022-09-15. Upper bounds on the Natarajan dimensions of some function classes. https://arxiv.org/abs/2209.07015

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