Sparse Greedy Minimax Probability Machine Classification

The Minimax Probability Machine Classification (MPMC) framework [Lanckriet et al., 2002] builds classifiers by minimizing the maximum probability of misclassification, and gives direct estimates of the probabilistic accuracy bound Ω. The only assumptions that MPMC makes is that good estimates of means and covariance matrices of the classes exist. However, as with Support Vector Machines, MPMC is computationally expensive and requires extensive cross validation experiments to choose kernels and kernel parameters that give good performance. In this paper we address the computational cost of MPMC by proposing an algorithm that constructs nonlinear sparse MPMC (SMPMC) models by incrementally adding basis functions (i.e.