A theoretical framework for decision trees in uncertain domains: Application to medical data sets

Experimental evidence shows that many attribute selection criteria involved in the induction of decision trees perform comparably. We set up a theoretical framework that explains this empirical law. It furthermore provides an infinite set of criteria (the C.M. criteria) which contains the most commonly used criteria. We also define C.M. pruning which is suitable in uncertain domains. In such domains, like medicine, some sub-trees which don't lessen the error rate can be relevant to point out some populations of specific interest or to give a representation of a large data file. C.M. pruning allows to keep such sub-trees, even when keeping the sub-trees doesn't increase the classification efficiency. Thus we obtain a consistent framework for both building and pruning decision trees in uncertain domains. We give typical examples in medicine, highlighting routine use of induction in this domain even if the targeted diagnosis cannot be reached for many cases from the findings under investigation.