This paper addresses the general problem of modelling and learning rank data
with ties. We propose a probabilistic generative model, that models the process
as permutations over partitions. This results in super-exponential
combinatorial state space with unknown numbers of partitions and unknown
ordering among them. We approach the problem from the discrete choice theory,
where subsets are chosen in a stagewise manner, reducing the state space per
each stage significantly. Further, we show that with suitable parameterisation,
we can still learn the models in linear time. We evaluate the proposed models
on the problem of learning to rank with the data from the recently held Yahoo!
challenge, and demonstrate that the models are competitive against well-known
rivals.Comment: 19 pages, 2 figure