On least trimmed squares neural networks

In this paper, least trimmed squares (LTS) estimators, frequently used in robust (or resistant) linear parametric regression problems, will be generalized to nonparametric LTS neural networks for nonlinear regression problems. Emphasis is put particularly on the robustness against outliers. This provides alternative learning machines when faced with general nonlinear learning problems. Simple weight updating rules based on gradient descent and iteratively reweighted least squares (IRLS) algorithms will be provided. The important parameter of trimming percentage for the data at hand can be determined by cross validation. Some simulated and real-world data will be used to illustrate the use of LTS neural networks. We will compare the robustness against outliers for usual neural networks with least squares criterion and the proposed LTS neural networks. Simulation results show that the LTS neural networks proposed in this paper have good robustness against outliers. Nonparametric least trimmed squares neural networks are proposed.We emphasize the issue of robustness against outliers.The trimming percentage for the data at hand is determined by cross validation.