We study the problem of collaborative filtering where ranking information is
available. Focusing on the core of the collaborative ranking process, the user
and their community, we propose new models for representation of the underlying
permutations and prediction of ranks. The first approach is based on the
assumption that the user makes successive choice of items in a stage-wise
manner. In particular, we extend the Plackett-Luce model in two ways -
introducing parameter factoring to account for user-specific contribution, and
modelling the latent community in a generative setting. The second approach
relies on log-linear parameterisation, which relaxes the discrete-choice
assumption, but makes learning and inference much more involved. We propose
MCMC-based learning and inference methods and derive linear-time prediction
algorithms