Learning Hierarchical Riffle Independent Groupings from Rankings

Ri ed independence is a generalized notion of probabilistic independence that has been shown to be naturally applicable to ranked data. In the ri ed independence model, one assigns rankings to two disjoint sets of items independently, then in a second stage, interleaves (or ri es) the two rankings together to form a full ranking, as if by shu ing a deck of cards. Because of this interleaving stage, it is much more di cult to detect ri ed independence than ordinary independence. In this paper, we provide the rst automated method for discovering sets of items which are ri e independent from a training set of rankings. We show that our clustering-like algorithms can be used to discover meaningful latent coalitions from real preference ranking datasets and to learn the structure of hierarchically decomposable models based on ri ed independence.