A Formulation for Minimax Probability Machine Regression

We formulate the regression problem as one of maximizing the minimum probability, symbolized by Ω, that future predicted outputs of the regression model will be within some ε bound of the true regression function. Our formulation is unique in that we obtain a direct estimate of this lower probability bound Ω. The proposed framework, minimax probability machine regression (MPMR), is based on the recently described 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 Ω bound, and the efficacy of the regression models.