Abstract
In this study, a modified monotone kernel regression (MonKR) method is proposed that integrates monotonicity knowledge with kernel regression. In MonKR, monotonicity knowledge is described by the first order difference inequality constraints on the kernel expansion, which are added directly to the kernel regression formulation to obtain a convex optimization problem. MonKR is solved by quadratic programming. An analysis of the number of added constraints showed that MonKR is monotonic provided that a small finite set of constraints on some discrete points is added to the kernel regression (KR) formulation, and the step length value of MonKR is suggested. MonKR is simple to use and it readily obtains monotonicity. A function approximation problem was used to demonstrate the monotonicity of MonKR and its predictive performance was better than or equal to some state-of-art methods. Furthermore, MonKR was used to determine the true boiling point curve of crude oil. The results demonstrated that monotonicity was obtained by MonKR and that the overall predictive performance of MonKR was better than that of some previous methods.
