$\ell_{\infty}$ Vector Contraction for Rademacher Complexity
Abstract
We show that the Rademacher complexity of any $\mathbb{R}^{K}$-valued function class composed with an $\ell_{\infty}$-Lipschitz function is bounded by the maximum Rademacher complexity of the restriction of the function class along each coordinate, times a factor of $\tilde{O}(\sqrt{K})$.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2019
- DOI:
- 10.48550/arXiv.1911.06468
- arXiv:
- arXiv:1911.06468
- Bibcode:
- 2019arXiv191106468F
- Keywords:
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- Computer Science - Machine Learning;
- Mathematics - Statistics Theory;
- Statistics - Machine Learning
- E-Print:
- Technical note