Model building using bi-level optimization

In many problems from different disciplines such as engineering, physics, medicine, and biology, a series of experimental data is used in order to generate a model that can describe a system with minimum noise. The procedure for building a model provides a description of the behavior of the system under study and can be used to give a prediction for the future. Herein a novel hierarchical bi-level implementation of the cross validation method is presented. In this bi-level schema, the leader optimization problem builds (training) the model and the follower checks (testing) the developed model. The problem of synthesis and analysis of regulatory networks is used to compare the classical cross validation method to the proposed methodology referred to as bi-level cross validation. In all the examples considered, the bi-level cross validation results in a better model compared with the classical cross validation approach.