Nonparametric classification with polynomial MPMC cascades

Abstract

A new class of nonparametric algorithms for high-dimensional binary classification is proposed using cascades of low dimensional polynomial structures. Construction of polynomial cascades is based on Minimax Probability Machine Classification (MPMC), which results in direct estimates of classification accuracy, and provides a simple stopping criteria that does not require expensive cross-validation measures. This Polynomial MPMC Cascade (PMC) algorithm is constructed in linear time with respect to the input space dimensionality, and linear time in the number of examples, making it a potentially attractive alternative to algorithms like support vector machines and standard MPMC. Experimental evidence is given showing that, compared to state-of-the-art classifiers, PMCs are competitive; inherently fast to compute; not prone to overfitting; and generally yield accurate estimates of the maximum error rate on unseen data.