Learn More about Your Data: A Symbolic Regression Knowledge Representation Framework

Abstract

In this paper, we propose a flexible knowledge representation framework which utilizes Symbolic Regression to learn and mathematical expressions to represent the knowledge to be captured from data. In this approach, learning algo- rithms are used to generate new insights which can be added to domain knowledge bases supporting again symbolic regression. This is used for the generalization of the well-known regression analysis to fulfill supervised classification. The approach aims to produce a learning model which best separates the class members of a labeled training set. The class boundaries are given by a separation surface which is represented by the level set of a model function. The separa- tion boundary is defined by the respective equation. In our symbolic approach, the learned knowledge model is repre- sented by mathematical formulas and it is composed of an optimum set of expressions of a given superset. We show that this property gives human experts options to gain additional insights into the application domain. Furthermore, the representation in terms of mathematical formulas (e.g., the analytical model and its first and second derivative) adds additional value to the classifier and enables to answer questions, which sub-symbolic classifier approaches cannot. The symbolic representation of the models enables an interpretation by human experts. Existing and previously known ex- pert knowledge can be added to the developed knowledge representation framework or it can be used as constraints. Additionally, the knowledge acquisition framework can be repeated several times. In each step, new insights from the search process can be added to the knowledge base to improve the overall performance of the proposed learning algo- rithms.