Correcting Binary Imprecise Classifiers: Local vs Global Approach

Abstract

This paper proposes a simple strategy for combining binary classifiers with imprecise probabilities as outputs. Our combination strategy consists in computing a set of probability distributions by solving an optimization problem whose constraints depend on the classifiers outputs. However, the classifiers may provide assessments that are jointly incoherent, in which case the set of probability distributions satisfying all the constraints is empty. We study different correction strategies for restoring this consistency, by relaxing the constraints of the optimization problem so that it becomes feasible. In particular, we propose and compare a global strategy, where all constraints are relaxed to the same level, to a local strategy, where some constraints may be relaxed more than others. The local discounting strategy proves to give very good results compared both to single classifier approaches and to classifier combination schemes using a global correction scheme.