Primal-Dual Monotone Kernel Regression

Authors:
K. Pelckmans;M. Espinoza;J. Brabanter;J. A. Suykens;B. Moor
Affiliations:
K.U. Leuven, ESAT-SCD-SISTA, Leuven, Belgium B-3001;K.U. Leuven, ESAT-SCD-SISTA, Leuven, Belgium B-3001;Departement Industrieel Ingenieur, Hogeschool KaHo Sint-Lieven (Associatie KULeuven), Belgium;K.U. Leuven, ESAT-SCD-SISTA, Leuven, Belgium B-3001;K.U. Leuven, ESAT-SCD-SISTA, Leuven, Belgium B-3001
Venue:
Neural Processing Letters
Year:
2005

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Abstract

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.