Some probabilistic modelling ideas for Boolean classification in genetic programming

Abstract

We discuss the problem of boolean classification via Genetic Programming. When predictors are numeric, the standard approach proceeds by classifying according to the sign of the value provided by the evaluated function. We consider an alternative approach whereby the magnitude of such a quantity also plays a role in prediction and evaluation. Specifically, the original, unconstrained value is transformed into a probability value which is then used to elicit the classification. This idea stems from the well-known logistic regression paradigm and can be seen as an attempt to squeeze all the information in each individual function. We investigate the empirical behaviour of these variants and discuss a third evaluation measure equally based on probabilistic ideas. To put these ideas in perspective, we present comparative results obtained by alternative methods, namely recursive splitting and logistic regression.