Nonparametric data selection for improvement of parametric neural learning: A cumulant-surrogate method

Abstract

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 significance discriminating between the original data and a set of scrambled surrogate data which correspond to the null hypothesis of a non-causal relationship between past and present. In this formulation nonlinear and non-Gaussian temporal 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 in this fashion the learning of irrelevant noise which normally spoils the generalization characteristics of the neural network.