Variance Stabilizing Regression Ensembles for Environmental Models

This paper describes linear regression models fitted for the 2006 predictive uncertainty in environmental modelling competition hosted at the WCCI 2006 conference. Entries into this competition are required to produce models of up to four non-linear regression problems. Rather than adopt a complex non-linear modelling technique, our approach is to fit linear models to transformed data, with adaptive methods used for setting parameters and estimating error. This paper describes several techniques popular with statisticians which are less well known in the computational intelligence community, then proposes new ways of using these statistics. We describe standard statistical transformation techniques, Yeo-Johnson and Box-Tidwell, and present stepwise algorithms for using these transformations on large data sets. These stepwise algorithms utilise the Anscombe procedure, runs tests on residuals, the Goldfeld-Quandt procedure and the Kolomogorov-Smirnoff test for normality. We combine these statistics with the transformation procedures to form a piecewise linear approach to environmental modelling.