Nonparametric Data Selection for Improvement of Parametric Neural Learning: A Cumulant-Surrogate Method

摘要

We introduce a nonparametric cumulant based statistical approach for detecting linear and nonlinear statistical dependences in non-stationary time series. The statistical dependence is detected by measuring the predictability which tests the null hypothesis of statistical independence, expressed in Fourier-space, by the surrogate method. Therefore, the predictability is defined as a higher-order cumulant based isgnificance discriminating between the original data and a set of scrambled surrogate data which correspond to the null hypothesis of a non-caual relationship between past and present. In this formulation nonlinear and non-Gaussian temproal dependences can be detected in time series. Information about the predictability can be used for example to select regions where a temporal structure is visible in order to select data for training a neural network for prediction. The regions where only a noisy behavior is observed are therefore ignored avoiding i this fashion the learning of irrelevant noise which normally spoils the generalization characteristics of the neural network.