A Formulation for Minimax Probability Machine Regression

Abstract

We formulate the regression problem as one of maximizing the mini-mum probability, symbolized by, that future predicted outputs of the regression model will be within some " bound of the true regression function. Our formulation is unique in that we obtain a direct estimate of this lower probability bound. The proposed framework, minimax probability machine regression (MPMR), is based on the recently de-scribed minimax probability machine classification algorithm [Lanckriet et al.] and uses Mercer Kernels to obtain nonlinear regression models. MPMR is tested on both toy and real world data, verifying the accuracy of the bound, and the efficacy of the regression models. 1