Learning From Ordered Sets and Applications in Collaborative Ranking

TL;DR

This paper introduces a probabilistic model for ordered sets, addressing the complex combinatorial problem of set partitioning and ordering, with applications in collaborative ranking and filtering.

Contribution

It develops a log-linear probabilistic model over ordered sets and proposes an efficient split-and-merge MCMC inference method, including latent variables for hidden data aspects.

Findings

Model is effective on large-scale collaborative filtering tasks.

The split-and-merge MCMC method efficiently explores the complex state space.

The approach is competitive with state-of-the-art methods.

Abstract

Ranking over sets arise when users choose between groups of items. For example, a group may be of those movies deemed $5$ stars to them, or a customized tour package. It turns out, to model this data type properly, we need to investigate the general combinatorics problem of partitioning a set and ordering the subsets. Here we construct a probabilistic log-linear model over a set of ordered subsets. Inference in this combinatorial space is highly challenging: The space size approaches $(N!/2)6.93145^{N+1}$ as $N$ approaches infinity. We propose a \texttt{split-and-merge} Metropolis-Hastings procedure that can explore the state-space efficiently. For discovering hidden aspects in the data, we enrich the model with latent binary variables so that the posteriors can be efficiently evaluated. Finally, we evaluate the proposed model on large-scale collaborative filtering tasks and demonstrate that it is competitive against state-of-the-art methods.