Quality assessment of a supervised multilabel classification rule with performance constraints

A multilabel classification rule with performance constraints for supervised problems is presented. It takes into account three concerns: the loss function which defines the criterion to minimize, the decision options which are defined by the admissible assignment classes or subsets of classes, and the constraints of performance. The classification rule is determined using an estimation of the conditional probability density functions and by solving an optimization problem. A criterion for assessing the quality of the rule and taking into account the loss function and the issue of the constraints is proposed. An example is provided to illustrate the classification rule and the relevance of the criterion.