University of Washington - Department of Statistics
People often express their preferences for web pages, products, candidates in an election as a ranked list. Ranked lists are also the standard output of search engines like Google or Sequest. The interest of this talk is to show how one can do "statistics as usual" with this kind of discrete, structured, high-dimensional data.
I will define statistical models over spaces of permutations and partial orderings, and present methods for estimating these models from data.
I will briefly describe the Maximum Likelihood problem and an algorithm for solving it. Then I will focus on recent work in Bayesian estimation for a class of widely used models called Mallows models. These models have continuous parameters representing the spread of the distribution and discrete parameters representing a central permutation. Therefore they raise extremely interesting statistical and computational challenges. I will describe the conjugate prior for this model class, and Monte Carlo algorithms for effectively sampling from the posterior, with application to preference data.
Joint work with: Harr Chen, Alnur Ali, Bhushan Mandhani, Le Bao, Kapil Phadnis, Arthur Patterson, and Jeff Bilmes.