A probability model for combining ranks

Mixed Group Ranks is a parametric method for combining rank based classifiers that is effective for many-class problems. Its parametric structure combines qualities of voting methods with best rank approaches. In [1] the parameters of MGR were estimated using a logistic loss function. In this paper we describe how MGR can be cast as a probability model. In particular we show that using an exponential probability model, an algorithm for efficient maximum likelihood estimation of its parameters can be devised. While casting MGR as an exponential probability model offers provable asymptotic properties (consistency), the interpretability of probabilities allows for flexiblity and natural integration of MGR mixture models.