RCGA-S/RCGA-SP Methods to Minimize the Delta Test for Regression Tasks Fernando Mateo 1 , Du˘ san Sovilj 2 , Rafael Gadea 1 , and Amaury Lendasse 2 1 Institute of Applications of Information Technologies and Advanced Communications, Polytechnic University of Valencia, Spain fermaji@upvnet.upv.es,rgadea@eln.upv.es 2 Laboratory of Information and Computer Science, Helsinki University of Technology, Finland dusans@cis.hut.fi,lendasse@hut.fi Abstract. Frequently, the number of input variables (features) involved in a problem becomes too large to be easily handled by conventional machine-learning models. This paper introduces a combined strategy that uses a real-coded genetic algorithm to find the optimal scaling (RCGA-S) or scaling + projection (RCGA-SP) factors that minimize the Delta Test criterion for variable selection when being applied to the input variables. These two methods are evaluated on five different re- gression datasets and their results are compared. The results confirm the goodness of both methods although RCGA-SP performs clearly bet- ter than RCGA-S because it adds the possibility of projecting the input variables onto a lower dimensional space. Key words: real-coded genetic algorithm, global search, variable selec- tion, delta test, input scaling, input projection 1 Introduction The size of datasets often compromises the models that can employ them for a determined regression or classification task. A linear increase in the number of variables results in an exponential increase in the necessary number of sam- ples to successfully represent the solution space. This burden is called curse of dimensionality [1] and affects many real-life problems usually characterized by a high number of features. In these cases, it is highly convenient to reduce the number of involved features in order to reduce the complexity of the required models and to improve the interpretability. In the recent years, many studies have intended to address variable selection for regression using a variety of search strategies and convergence criteria. One of the most successful criteria to determine the optimal set of variables in regression applications is a nonparametric noise estimator called Delta Test (DT) ([2], [3]). With regard to the search strategy, some authors propose local search strate- gies for DT minimization (e.g. forward search [4], backward search, forward- backward search ([5], [6])), because of their high speed, but they suffer from se- vere sensitivity to local minima. Global search strategies (e.g. exhaustive search,