Integrating Interpolation and Extrapolation: A Hybrid Predictive Framework for Supervised Learning

In the domain of supervised learning, interpolation and extrapolation serve as crucial methodologies for predicting data points within and beyond the confines of a given dataset, respectively. The efficacy of these methods is closely linked to the nature of the dataset, with increased challenges when multivariate feature vectors are handled. This paper introduces a novel prediction framework that integrates interpolation and extrapolation techniques. Central to this method are two main innovations: an optimization model that effectively classifies new multivariate data points as either interior or exterior to the known dataset, and a hybrid prediction system that combines k-nearest neighbor (kNN) and linear regression. Tested on the port state control (PSC) inspection dataset at the port of Hong Kong, our framework generally demonstrates superior precision in predictive outcomes than traditional kNN and linear regression models. This research enriches the literature by illustrating the enhanced capability of combining interpolation and extrapolation techniques in supervised learning.