Thomas Strohmann, Gregory Grudic
We formulate the regression problem as one of maximizing the mini- mum probability, symbolized by (cid:10), that future predicted outputs of the regression model will be within some (cid:6)" bound of the true regression function. Our formulation is unique in that we obtain a direct estimate of this lower probability bound (cid:10). 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 (cid:10) bound, and the efﬁcacy of the regression models.