Efficient and Accurate Learning of Mixtures of Plackett-Luce Models

TL;DR

This paper introduces a novel initialization and EM algorithm for mixture of Plackett-Luce models, improving accuracy and efficiency over existing methods, especially with large item sets.

Contribution

It presents a provably accurate initialization method and an EM algorithm that maximizes the true likelihood efficiently for mixture PL models.

Findings

Outperforms baseline algorithms in accuracy and speed

Effective on large item datasets

Provides theoretical guarantees for initialization

Abstract

Mixture models of Plackett-Luce (PL) -- one of the most fundamental ranking models -- are an active research area of both theoretical and practical significance. Most previously proposed parameter estimation algorithms instantiate the EM algorithm, often with random initialization. However, such an initialization scheme may not yield a good initial estimate and the algorithms require multiple restarts, incurring a large time complexity. As for the EM procedure, while the E-step can be performed efficiently, maximizing the log-likelihood in the M-step is difficult due to the combinatorial nature of the PL likelihood function (Gormley and Murphy 2008). Therefore, previous authors favor algorithms that maximize surrogate likelihood functions (Zhao et al. 2018, 2020). However, the final estimate may deviate from the true maximum likelihood estimate as a consequence. In this paper, we address these known limitations. We propose an initialization algorithm that can provide a provably accurate initial estimate and an EM algorithm that maximizes the true log-likelihood function efficiently. Experiments on both synthetic and real datasets show that our algorithm is competitive in terms of accuracy and speed to baseline algorithms, especially on datasets with a large number of items.