A study on majority-voting classifiers with guarantees on the probability of error

The Guaranteed Error Machine (GEM) is a classification algorithm that allows the user to set a-priori (i.e., before data are observed) an upper bound on the probability of error. Due to its strong statistical guarantees, GEM is of particular interest for safety critical applications in control engineering. Empirical studies have suggested that a pool of GEM classifiers can be combined in a majority voting scheme to boost the individual performances. In this paper, we investigate the possibility of keeping the probability of error under control in the absence of extra validation or test sets. In particular, we consider situations where the classifiers in the pool may have different guarantees on the probability of error, for which we propose a data-dependent weighted majority voting scheme. The preliminary results presented in this paper are very general and apply in principle to any weighted majority voting scheme involving individual classifiers that come with statistical guarantees, in the spirit of Probably Approximately Correct (PAC) learning.