Model Selection for Regression with Continuous Kernel Functions Using the Modulus of Continuity

This paper presents a new method of model selection for regression problems using the modulus of continuity. For this purpose, we suggest the prediction risk bounds of regression models using the modulus of continuity which can be interpreted as the complexity of functions. We also present the model selection criterion referred to as the modulus of continuity information criterion (MCIC) which is derived from the suggested prediction risk bounds. The suggested MCIC provides a risk estimate using the modulus of continuity for a trained regression model (or an estimation function) while other model selection criteria such as the AIC and BIC use structural information such as the number of training parameters. As a result, the suggested MCIC is able to discriminate the performances of trained regression models, even with the same structure of training models. To show the effectiveness of the proposed method, the simulation for function approximation using the multi-layer perceptrons (MLPs) was conducted. Through the simulation for function approximation, it was demonstrated that the suggested MCIC provides a good selection tool for nonlinear regression models, even with the limited size of data.