Minimizing the expected costs of classifying patterns by sequential costly inspections

In many applications, an expert classifier system has access to statistical information about the prior probabilities of the different classes. Such information should in principle reduce the amount of additional information that the system must collect, e.g., from answers to questions, before it can make a correct classification. This paper examines how to make best use of such prior statistical information, sequentially updated by collection of additional costly information, to optimally reduce uncertainty about the class to which a case belongs, thus minimizing the cost or effort required to correctly classify new cases. Two approaches are introduced, one motivated by information theory and the other based on the idea of trying to prove class membership as efficiently as possible. It is shown that, while the general problem of cost-effective classification is NP-hard, both heuristics provide useful approximations on small to moderate sized problems. Moreover, a hybrid heuristic that chooses which approach to apply based on the characteristics of the classification problem (entropy of the class probability distribution and coefficient of variation of information collection costs) appears to give excellent results. The results of initial computational experiments are summarized in support of these conclusions.