Evaluation of the Neural-network-based Method to Discover Sets and Representatives of Nonlinearly Dependent Variables

It is desired in a variety of fields to identify which variables are dependent, and variable dependence measures have been studied. The majority of such measures detect a linear or a certain range of nonlinear dependence between paired variables. To go beyond them, a method based on Neural Network Regression, Group Lasso, and Information Aggregation has been proposed in our past study. It can detect a wide range of nonlinear dependences among multi variables and discover the sets and representatives of the detected dependences. Its fundamental effectiveness has already been examined using synthesized artificial datasets containing a single dependence. For further evaluation in the present study, we conducted an experiment using those containing multi dependences. The proposed method succeeded in discovering the sets and representatives, and its performance was robust to data size and noise rate. The experimental results suggested that the proposed method works well for difficult tasks to handle multi dependences.