Discovering Nonlinear Integral Networks from Databases Using Evolutionary Computation and Minimum Description Length Principle

By using a non-additive set function to describe the interaction among variables, a nonlinear non-negative multi-regression is established based on the Choquet integral with respect to the set function. We generalize this nonlinear model and propose a novel formalism that provides an effective and efficient reasoning procedure to perform information fusion, decision making, and medical diagnoses. In the formalism, a network structure and a number of Choquet integrals are used to represent the relationships among variables. We propose a new algorithm to learn the network structure and the regression parameters of Choquet integrals from training examples in databases. The algorithm is based on the minimum description length (MDL) principle and evolutionary programming (EP). We conduct a series of experiments to demonstrate the performance of our algorithm and estimate the effectiveness of the MDL metric and the genetic operators. The empirical results illustrate that our algorithm can successfully discover the target network structure and the regression parameter.