Bayes covariant multi-class classification

Defining notion of Bayes covariance.Proving existence and uniqueness of Bayes covariant classifier of 3 categories.Explicit construction of a Bayes covariant classifier for any number of categories.A proof that previously considered methods are not Bayes covariant.Comparison of various methods for combining pairwise classifiers via MDS, and speech frame classification. We consider multi-class classification models built from complete sets of pairwise binary classifiers. The BradleyTerry 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.