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.

翻译：贝叶斯Mallows模型是一种灵活的分析工具，适用于处理完整或部分排序数据，以及传递性或非传递性的成对偏好数据。在偏好学习的众多潜在应用中，数据往往以序贯方式到达，基于当前可用数据高效更新后验信念与预测具有重要的实际意义。尽管如此，现有算法大多集中于批量推断。本文提出一种基于嵌套序贯蒙特卡罗的方法，用于序贯估计贝叶斯Mallows模型的后验分布。该算法仅需极少以调参形式呈现的用户输入，易于并行化实现，且能直接输出边际似然作为估计的副产品，因此在批量估计场景中也可作为马尔可夫链蒙特卡罗技术的有效替代方案。