Abstract—CoReJava (Constraint Optimization Regression in Java) is a framework which extends the programming language Java with built-in regression analysis, i.e., the capability to do parameter estimation for a function. CoReJava is unique in that functional forms for regression analysis are expressed as first-class citizens, i.e., 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 CoReJava include calibration of parameters of computational processes, described as OO programs. If-then-else structures of Java language are naturally adopted to create piecewise functional forms of regression. Thus, minimization of the sum of least squared errors involves an optimization problem with a search space that is exponential to the size of learning set. In this paper, combinatorial restructuring algorithm is proposed to guarantee learning optimality and furthermore reduce the search space to be polynomial in the size of learning set, but exponential to the number of piece-wise bounds. Heaviside restructuring algorithm, which expresses the piecewise linear regression function using a unified functional format, instead of multiple pieces, is proposed to decrease the searching complexity further to be polynomial in both the size of learning set and the number of piece-wise bounds, while the learning outcome will be an approximation of the optimality.
Index Terms—Combinatorial Restructuring, Heaviside Restructuring, Object-Oriented Programming, Piecewise Regression
Juan Luo is with the Dept. of Computer Science, George Mason University, Fairfax, VA 22030, USA (corresponding author to provide phone: 703-993-1531; e-mail: email@example.com). Alexander Brodsky is with Dept. of Computer Science, George Mason University, Fairfax, VA 22030, USA (e-mail: Brodsky@gmu.edu)
Cite: Juan Luo and Alexander Brodsky, "Piecewise Regression Learning in CoReJava Framework," International Journal of Machine Learning and Computing vol. 1, no. 2, pp. 163-169, 2011.