Choquet Integral in Decision Making and Metric Learning

摘要

Choquet integrals are an effective tool for aggregation of numerical data. From a mathematical point of view they generalize the Lebesgue integral when the measure is not additive. Non-additivity permits us to represent interactions that cannot be represented by additive measures. Choquet integrals have been used in a large variety of contexts that include decision making, computer vision, and economy. In this talk we will illustrate their use in decision making. We will review some results on Choquet integral based probability-density functions, which can be used to model decision making and classification problems. This will lead us to consider distances based on the Choquet integral, and the problem of measure identification. This last problem corresponds to metric learning. We will show its use in risk assessment in data privacy.