On the Error Resistance of Hinge-Loss Minimization
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/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.
Apple sponsored the Neural Information Processing Systems (NeurIPS) conference, which was held virtually from December 6 to 12. NeurIPS is a global conference focused on fostering the exchange of research on neural information processing systems in their biological, technological, mathematical, and theoretical aspects.