Angle-Based Models for Ranking Data

TL;DR

This paper introduces angle-based exponential ranking models that utilize a consensus score vector and cosine similarity, employing Bayesian variational inference for efficient and scalable ranking data analysis, including extensions for incomplete and mixture models.

Contribution

The paper proposes a novel angle-based ranking model with Bayesian variational inference, offering computational efficiency and scalability for large and complex ranking datasets.

Findings

Bayesian variational inference outperforms MCMC in speed and avoids overfitting.

Model effectively handles large item sets and incomplete rankings.

Extensions to mixture models improve flexibility in ranking analysis.

Abstract

A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of the relative preference of the items. The probability of observing a ranking is modeled to be proportional to its cosine of the angle from the consensus vector. Bayesian variational inference is employed to determine the corresponding predictive density. It can be seen from simulation experiments that the Bayesian variational inference approach not only has great computational advantage compared to the traditional MCMC, but also avoids the problem of overfitting inherent when using maximum likelihood methods. The model also works when a large number of items are ranked which is usually an NP-hard problem to find the estimate of parameters for other classes of ranking models. Model extensions to incomplete rankings and mixture models are also developed. Real data applications demonstrate that the model and extensions can handle different tasks for the analysis of ranking data.