Symbolic Regression Via Genetic Programming as a Discovery Engine: Insights on Outliers and Prototypes

Abstract

In this chapter we illustrate a framework based on symbolic regression to generate and sharpen the questions about the nature of the underlying system and provide additional context and understanding based on multi-variate numeric data.

We emphasize the necessity to perform data modeling in a global approach, iteratively applying data analysis and adaptation, model building, and problem reduction procedures. We illustrate it for the problem of detecting outliers and extracting significant features from the CountryData¹-a data set of economic, political, social and geographic data collected. We present two complementary ways of extracting outliers from the data-the content-based and the model-based approach. The content-based approach studies the geometrical structure of the multi-variate data, and uses data-balancing algorithms to sort the data records in the order of decreasing typicalness, and identify the outliers as the least typical records before the modeling is applied to a data set. The model-based outlier detection approach uses symbolic regression via Pareto genetic programming (GP) to identify records which are systematically under-or over-predicted by diverse ensembles of (thousands of) global non-linear symbolic regression models.

Both approaches applied to the CountryData produce insights into outlier vs. prototypes division amongworld countries and about driving economic properties predicting gross domestic product (GDP) per capita.