True risk bounds for the regression of real-valued functions

This paper presents a new form of true risk bounds for the regression of real-valued functions. The goal of machine learning is minimizing the true risk (or general error) for the whole distribution of sample space, not just a set of training samples. However, the true risk cannot be estimated accurately with the finite number of samples. In this sense, we derive the form of true risk bounds which may provide the useful guideline for the optimization of learning models. Through the simulation for the function approximation, we have shown that the prediction of true risk bounds based on the suggested functional norm is well fitted to the empirical data.