Learning intersections of halfspaces with a margin

We give a new algorithm for learning intersections of halfspaces with a margin, i.e. under the assumption that no example lies too close to any separating hyperplane. Our algorithm combines random projection techniques for dimensionality reduction, polynomial threshold function constructions, and kernel methods. The algorithm is fast and simple. It learns a broader class of functions and achieves an exponential runtime improvement compared with previous work on learning intersections of halfspaces with a margin. Key words: computational learning theory, intersections of halfspaces, margin, polynomial threshold function, random projection, kernel Perceptron. ∗ Corresponding author