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arXiv · 2003.04180

Approximate is Good Enough: Probabilistic Variants of Dimensional and Margin Complexity

Pritish Kamath·Omar Montasser·Nathan Srebro
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Abstract

We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that such notions are not only sufficient for learning using linear predictors or a kernel, but unlike the exact variants, are also necessary. Thus they are better suited for discussing limitations of linear or kernel methods.

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Pritish Kamath, Omar Montasser, Nathan Srebro. 2020-03-09. Approximate is Good Enough: Probabilistic Variants of Dimensional and Margin Complexity. https://arxiv.org/abs/2003.04180

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