Do not match, inherit: fitness surrogates for genetics-based machine learning techniques

A byproduct benefit of using probabilistic model-building genetic algorithms is the creation of cheap and accurate surrogate models. Learning classifier systems -- and genetics-based machine learning in general -- can greatly benefit from such surrogates which may replace the costly matching procedure of a rule against large data sets. In this paper we investigate the accuracy of such surrogate fitness functions when coupled with the probabilistic models evolved by the $\chi$-ary extended compact classifier system ($\chi$eCCS). To achieve such a goal, we show the need that the probabilistic models should be able to represent all the accurate basis functions required for creating an accurate surrogate. We also introduce a procedure to transform populations of rules based into dependency structure matrices (DSMs) which allows building accurate models of overlapping building blocks -- a necessary condition to accurately estimate the fitness of the evolved rules.