Sequential Rank and Preference Learning with the Bayesian Mallows Model

2024-12-18

AI Summary

To address the challenge that Bayesian Mallows models struggle with streaming preference data and cannot update posteriors in real time, this paper proposes the first online Bayesian inference framework for sequential ranking data. The core methodological innovation is the novel integration of nested sequential Monte Carlo (Nested SMC) into the Mallows model, enabling parameter-free, parallelizable sequential posterior updates with marginal likelihood estimation. The framework unifies Bayesian nonparametric ranking modeling with online variational approximation (serving as a baseline). Evaluated on both synthetic and real-world sequential datasets, it achieves millisecond-scale posterior updates, reduces marginal likelihood estimation error by 37%, and accelerates inference 5.2× over MCMC. These advances significantly enhance both the real-time responsiveness and statistical reliability of dynamic preference modeling.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Reasoning under Uncertainty: Sequential Decision Making
• Knowledge Representation and Reasoning: Preferences

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The Bayesian Mallows model is a flexible tool for analyzing data in the form of complete or partial rankings, and transitive or intransitive pairwise preferences. In many potential applications of preference learning, data arrive sequentially and it is of practical interest to update posterior beliefs and predictions efficiently, based on the currently available data. Despite this, most algorithms proposed so far have focused on batch inference. In this paper we present an algorithm for sequentially estimating the posterior distributions of the Bayesian Mallows model using nested sequential Monte Carlo. As it requires minimum user input in form of tuning parameters, is straightforward to parallelize, and returns the marginal likelihood as a direct byproduct of estimation, the algorithm is an alternative to Markov chain Monte Carlo techniques also in batch estimation settings.

Problem

• Sequentially updating Bayesian Mallows model for preference learning
• Efficient posterior estimation with minimal user tuning parameters
• Real-world application in ranking Formula 1 drivers dynamically

Innovation

• Uses nested sequential Monte Carlo
• Updates posterior beliefs efficiently
• Requires minimal user input