Parameter estimation in geographically weighted regression

Abstract

Proposed and implemented is a regression framework, which extends the programming language Java with regression analysis, i.e., the capability to do parameter estimation for a function. The regression framework is unique in that functional forms for regression analysis are expressed as Java programs, in which some parameters are not a priori known, but need to be learned from training sets provided as input. Typical applications of this regression framework include calibration of parameters of computational processes, described as OO programs. To implement regression learning, the compiler of this framework (1) analyses the structure of the parameterized Java program that represents a functional form, (2) automatically generates a constraint optimization problem, in which constraint variables are the unknown parameters, and the objective function to be minimized is the sum of squares of errors with regarding to the training set, and (3) solves the optimization problem using an external nonlinear optimization solver. Then the framework executes as a regular Java program, in which the initially unknown parameters are replaced with the found optimal values. The syntax and semantics of the regression framework are formally defined and exemplified in the geographically weighted regression model.