Learning geometric concepts with nasty noise
Ilias Diakonikolas, Daniel M. Kane, Alistair M. Stewart · 2018
We study the efficient learnability of geometric concept classes — specifically, low-degree polynomial threshold functions (PTFs) and intersections of halfspaces — when a fraction of the training data is adversarially corrupted. We give the first polynomial-time PAC learning algorithms for these concept classes with dimension-independent error guarantees in the presence of nasty noise under the Gaussian distribution. In the nasty noise model, an omniscient adversary can arbitrarily corrupt a small fraction of both the unlabeled data points and their labels. This model generalizes well-studied noise models, including the malicious noise model and the agnostic (adversarial label noise) model. Prior to our work, the only concept class for which efficient malicious learning algorithms were known was the class of origin-centered halfspaces.