Hooke and Jeeves Pattern Search Method and Global Optimal Solution

Abstract

In Data Science, it is imperative to build a model that learns the parameters from the data itself to solve either predictive or prescriptive problems while ensuring improved fidelity of the solution. In this article, we propose to model the non-stationary present in the data in terms of spatial anisotropic interpolation which encapsulates the trend as polynomial regression and characterizes the associated error field as a Gaussian noise process. The fundamental emphasis of the paper lies in the minimization of anisotropic error by learning the model parameters using Hooke and Jeeve’s pattern search algorithm, a gradient-free pattern search algorithm and works even in missing value scenarios. The Design and Analysis of the Computer Experiments (DACE) based metaphor are developed and the quality of results are demonstrated on benchmark functions. The proposed implementation essentially has a wide range of applications in Computer Vision, weather prediction, Ore mining, etc.