Learning Halfspaces with Massart Noise Under Structured Distributions
Abstract
We study the problem of learning halfspaces with Massart noise in the distributionspecific PAC model. We give the first computationally efficient algorithm for this problem with respect to a broad family of distributions, including logconcave distributions. This resolves an open question posed in a number of prior works. Our approach is extremely simple: We identify a smooth {\em nonconvex} surrogate loss with the property that any approximate stationary point of this loss defines a halfspace that is close to the target halfspace. Given this structural result, we can use SGD to solve the underlying learning problem.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.05632
 Bibcode:
 2020arXiv200205632D
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Data Structures and Algorithms;
 Mathematics  Statistics Theory;
 Statistics  Machine Learning