This talk is concerned with summarizing - by means of statistical models - of data that expresses preferences. This data is typically a set of rankings of n items by a panel of experts; the simplest summary is the "consensus ranking", or the "centroid" of the set of rankings. Such problems appear in many tasks, ranging from combining voter preferences to boosting of search engines. We study the problem in its more general form of estimating a parametric model over permutations, known as the Generalized Mallows (GM) model. The talk will present a new exact estimation algorithm, non-polynomial in theory, but extremely effective in comparison with existing algorithms. From a statistical point of view, we show that the GM model is an exponential family, and introduce the conjugate prior for this model class. Then we introduce the infinite GM model, corresponding to "rankings" over an infinite set of items, and show that this model is both elegant and of practical significance. Finally, the talk will touch upon the subject of multimodal distributions and clustering. Joint work with: Bhushan Mandhani, Le Bao, Kapil Phadnis, Arthur Patterson and Jeff Bilmes.
Group for Research in Decision Analysis