On the Error Resistance of Hinge Loss Minimization

• URL: http://arxiv.org/abs/2012.00989v1
• Date: Wed, 2 Dec 2020 06:49:24 GMT
• Title: On the Error Resistance of Hinge Loss Minimization
• Authors: Kunal Talwar
• Abstract summary: We identify a set of conditions on the data under which surrogate loss minimization algorithms provably learn the correct classifier. In particular, we show that if the data is linearly classifiable with a slightly non-trivial margin, then surrogate loss minimization has negligible error on the uncorrupted data.
• Score: 30.808062097285706
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Commonly used classification algorithms in machine learning, such as support vector machines, minimize a convex surrogate loss on training examples. In practice, these algorithms are surprisingly robust to errors in the training data. In this work, we identify a set of conditions on the data under which such surrogate loss minimization algorithms provably learn the correct classifier. This allows us to establish, in a unified framework, the robustness of these algorithms under various models on data as well as error. In particular, we show that if the data is linearly classifiable with a slightly non-trivial margin (i.e. a margin at least $C/\sqrt{d}$ for $d$-dimensional unit vectors), and the class-conditional distributions are near isotropic and logconcave, then surrogate loss minimization has negligible error on the uncorrupted data even when a constant fraction of examples are adversarially mislabeled.

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