Primal-Dual Monotone Kernel Regression

This paper considers the estimation of monotone nonlinear regression functions based on Support Vector Machines (SVMs), Least Squares SVMs (LS-SVMs) and other kernel machines. It illustrates how to employ the primal-dual optimization framework characterizing LS-SVMs in order to derive a globally optimal one-stage estimator for monotone regression. As a practical application, this letter considers the smooth estimation of the cumulative distribution functions (cdf), which leads to a kernel regressor that incorporates a Kolmogorov–Smirnoff discrepancy measure, a Tikhonov based regularization scheme and a monotonicity constraint.