Probabilistic Safety Regions Via Finite Families of Scalable Classifiers
Alberto Carlevaro Teodoro Alamo Fabrizio Dabbene Maurizio Mongelli
Supervised classification recognizes patterns in the data to separate classes
of behaviours. Canonical solutions contain misclassification errors that are
intrinsic to the numerical approximating nature of machine learning. The data
analyst may minimize the classification error on a class at the expense of
increasing the error of the other classes. The error control of such a design
phase is often done in a heuristic manner. In this context, it is key to
develop theoretical foundations capable of providing probabilistic
certifications to the obtained classifiers. In this perspective, we introduce
the concept of probabilistic safety region to describe a subset of the input
space in which the number of misclassified instances is probabilistically
controlled. The notion of scalable classifiers is then exploited to link the
tuning of machine learning with error control. Several tests corroborate the
approach. They are provided through synthetic data in order to highlight all
the steps involved, as well as through a smart mobility application.