D-optimal plans for variable selection in data bases

Abstract

This paper is based on an article of Pumplun et al. (2005a) that investigates the use of Design of Experiments in data bases in order to select variables that are relevant for classification in situations where a sufficient number of measurements of the explanatory variables is available, but measuring the class label is hard, e. g. expensive or time-consuming. Pumplun et al. searched for D-optimal designs in existing data sets by means of a genetic algorithm and assessed variable importance based on the found plans. If the design matrix is standardized these D-optimal plans are almost orthogonal and the explanatory variables are nearly uncorrelated. Thus Pumplun et al. expected that their importance for discrimination can be judged independently of each other. In a simulation study Pumplun et al. applied this approach in combination with five classification methods to eight data sets and the obtained error rates were compared with those resulting from variable selection on the basis of the complete data sets. Based on the D-optimal plans in some cases considerably lower error rates were achieved. Although Pumplun et al. (2005a) obtained some promising results, it was not clear for different reasons if D-optimality actually is beneficial for variable selection. For example, D-efficiency and orthogonality of the resulting plans were not investigated and a comparison with variable selection based on random samples of observations of the same size as the D-optimal plans was missing. In this paper we extend the simulation study of Pumplun et al. (2005a) in order to verify their results and as basis for further research in this field. Moreover, in Pumplun et al. D-optimal plans are only used for data preprocessing, that is variable selection. The classification models are estimated on the whole data set in order to assess the effects of D-optimality on variable selection separately. Since the number of measurements of the class label in fact is limited one would normally employ the same observations that were used for variable selection for learning, too. For this reason in our simulation study the appropriateness of D-optimal plans for training classification methods is additionally investigated. It turned out that in general in terms of the error rate there is no difference between variable selection on the basis of D-optimal plans and variable selection on random samples. However, for training of linear classification methods D-optimal plans seem to be beneficial.