Advances in structural modeling robust to outliers in explanatory and response variables

The robust regression analysis works on data affected by deviations from a general assumption of normality. Currently the field of robust linear regression analysis is well developed and there are number of stable and verified by time methods. In contrast the robust structural modeling and high-order model parameter estimation are still under active development. This paper describes advances in the algorithm development designed to solve a task of optimal polynomial model selection on multivariate data sets in presence of outliers in both explanatory and response variables. Previous version of our robust Polynomial Neural Network (PNN) was addressed to the modeling of the data with outliers in response variable only. On one side novel algorithm is still based on GMDH-type PNN, which gives an universal model structure identification thanks to the evolving adaptively synthesized bounded network. And on the other side the algorithm is enhanced with GM-like estimator used for parameter estimation, which allows to achieve robustness to outliers in both explanatory and response data-sets. Enhanced RPNN was developed and tested on the artificial data-sets generated from polynomials of up to third degree. The Gaussian noise as well as outliers was added to the data. Enhanced RPNN demonstrated robustness to outliers in both explanatory and response variables (with 25% of outliers) and good accuracy of the automatic structure syntheses as well as of the parameters estimation.