Probabilistic Models over Ordered Partitions with Application in Learning to Rank

TL;DR

This paper introduces a probabilistic model for ranking data with ties, using permutations over partitions, and demonstrates its efficiency and competitiveness in learning to rank tasks.

Contribution

It presents a novel generative model for rank data with ties based on permutations over partitions, enabling linear-time learning.

Findings

Model is competitive on Yahoo! challenge data

Reduces complexity via stagewise subset selection

Achieves linear-time training with proper parameterization

Abstract

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.