Risk reduction for nonlinear prediction and its application to the surrogate data test

We propose a method for estimating nonlinear prediction risk using a bagging algorithm that involves ensemble learning. First we estimate the probability distribution of a future state as the ensemble set obtained using bagging predictors, and consider its standard deviation as the prediction risk. We can then improve the prediction reliability by avoiding dangerous predictions if the estimated prediction risk is high. As an application of this risk reduction method, we improve the power of surrogate data tests for system identification. Low prediction accuracy and poor system identification are caused by short and noisy data, so we perform simulations using short data derived from noisy chaotic models and real systems to confirm the validity of our method.