Estimation of error confidence intervals for the regression of real-valued functions

This paper presents a new method of estimating the error confidence interval defined by the absolute value of difference between the true (or general) and empirical risks for the regression of real-valued functions. The theoretical bounds of error confidence intervals can be derived in the sense of probably approximately correct (PAC) learning. However, these theoretical bounds are too overestimated and not well fitted to the empirical data. In this sense, a new estimation model of error confidence intervals which can explain the behavior of general error more faithfully to the given samples, is suggested. To show the validity of our model, the error confidence intervals for the approximation of 2-D function and the prediction of Mackey-Glass time series, are estimated and compared with the experimental results.