Constructing an influence function of robust learning algorithm based on error distributions for the neural networks

Various robust learning algorithms have been proposed in the literature to overcome the effects of outliers. In those learning algorithms, the robust learning algorithms are divided into two categories. One is directly adopts the theory of the M-estimator. The other is the least mean log square learning algorithm in which errors are assumed to be the Cauchy distribution. However, outliers not only affect the fatness, but also may slightly affect the skewness of the distribution. In the paper, the errors distribution is assumed to belong to the generalized exponential family and an adaptive robust learning algorithm is then proposed. The idea of our approach is to adaptively construct the influence function based on the current observed error distribution. Since the kurtosis can be used to measure the fatness of a distribution, it is employed for identifying a coefficient in the generalized exponential distribution family through the moment recursive relations. The proposed algorithm has been employed under various noise distributions and the results have demonstrated superiority over other robust learning algorithms