Cranking: Combining Rankings Using Conditional Probability Models on Permutations

A new approach to ensemble learning is introduced that takes ranking rather than classification as fundamental, leading to models on the symmetric group and its cosets. The approach uses a generalization of the Mallows model on permutations to combine multiple input rankings. Applications include the task of combining the output of multiple search engines and multiclass or multilabel classification, where a set of input classifiers is viewed as generating a ranking of class labels. Experiments for both types of applications are presented.