Multilabel Classification Rule with Performance Constraints

A formulation for multilabel and performance constraints classification problems is presented within the framework of statistical decision theory. The definition of the problem takes into account three concerns. The first is the cost function which defines the criterion to minimize; the second is the decision options which are defined by the admissible assignment classes or subsets of classes and the third one is the constraints of performance. Assuming that the conditional probability density functions are known, the classification rule that is solution of the stated problem is expounded. Two examples are provided to illustrate the formulation and the decision rule obtained