On the robustness of the Olanrewaju-Olanrewaju regression kernel-based to nonparametric kernels for Support Vector Regressor (SVR)
Abstract:{In this article we studied and juxtaposed nonparametric Least Square and the Olanrewaju-Olanrewaju regression-type \({L_{(O – O){\lambda _{\gamma (\left| \theta \right|)}}}}\) kernels for supervised Support Vector Regressor (SVR) machine learning of hyperplane regression in a bivariate setting. The nonparametric kernels used to expound the SVR were Bisquare, Gaussian, Triweight, Uniform, Epanechnikov, and Triangular. Lagrangian multiplier estimation technique was adopted in estimating the involved SVR hyperplane regression coefficients as well as other embedded coefficients in each of the stated kernels. In addition, point estimate of the Euclidean distance (\(r\)) and error margin (\(d\)) in each of the SVR kernels were carved-out. In demonstration to the annual birthrate and its percentage change (\(\Delta \% \)) of the Nigeria populace from 1950 to 2023, the Olanrewaju-Olanrewaju regression-type kernel for SVR robustly outperformed the nonparametric and Least Square kernel-based SVRs with a miniature Cross-Validation index of -1205.49. 5.9% and 3.2% hyperplane estimated regression coefficients from the Olanrewaju-Olanrewaju kernel-based SVR were recorded for the annual birthrate and its percentage change (\(\Delta \% \)) respectively. Interpretably, this connotes that for every one percent increment in the annual birthrate per 1000, the mean rate of the Nigeria populace from 1950 to 2023 increased by 5.9% while other variables were held constant. Similarly, its percentage change per 1000 increased by 3.2% while other variables were held constant. In recommendation, the nonparametric and Olanrewaju-Olanrewaju regression-type SVRs as well as the Least Square SVR were pinpointed for future consideration of categorical, missing and zero bivariate observations.
