Bayes covariant multi-class classification

We consider multi-class classification models built from complete sets of pairwise binary classifiers. The Bradley-Terry model is often used to estimate posterior distributions in this setting. We introduce the notion of Bayes covariance, which holds if the multi-class classifier respects multiplicative group action on class priors. As a consequence, a Bayes covariant method yields the same result whether new priors are considered before or after combination of the individual classifiers, which has several practical advantages for systems with feedback. In the paper, we construct a Bayes covariant combining method and compare it with previously published methods in both Monte Carlo simulations as well as on a practical speech frame recognition task.