Model Selection in Regression Problems Based on the Modulus of Continuity

TL;DRAbstract

This paper presents a new method of model selection in regression problems based on the modulus of continuity. For this purpose, the bounds on the expected risks are suggested using the modulus of continuity for the target and estimation functions. As a result, the suggested bounds are described by learned parameters of regression models and the model selection criteria referred to as the modulus of continuity information criteria (MCIC) are suggested for the selection of optimal structure of regression models. Through the simulation for function approximation, we have shown that the suggested model selection can provide a better performance than other statistical methods of model selection such as AIC or BIC from the view points of the risks and the number of parameters.

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