Discovery of Sets and Representatives of Variables in Co-nonlinear Relationships by Neural Network Regression and Group Lasso

In regression and classification, the dependences among input variables lead to the reduction in prediction performance and reliability and to the misidentification of contributable input variables. Not only for these issues but also knowledge discovery, it is necessary to clarify variable dependences. This study aims to discover the sets and representatives of co-nonlinear variables, ensuring a high nonlinearity modeling capability and a high reproducibility without variable combinational explosion. Our proposed method achieves this by combining neural network regression, group lasso, and complementary aggregation of regression results. We conducted experiments to examine the fundamental effectiveness of the proposed method, using synthetic data of which co-nonlinearities were known. As a result, the proposed method succeeded to discover the sets and representatives of co-nonlinear variables robustly to noise added to the variables.