Rank-based Bayesian clustering via covariate-informed Mallows mixtures
arxiv(2023)
摘要
Data in the form of rankings, ratings, pair comparisons or clicks are
frequently collected in diverse fields, from marketing to politics, to
understand assessors' individual preferences. Combining such preference data
with features associated with the assessors can lead to a better understanding
of the assessors' behaviors and choices. The Mallows model is a popular model
for rankings, as it flexibly adapts to different types of preference data, and
the previously proposed Bayesian Mallows Model (BMM) offers a computationally
efficient framework for Bayesian inference, also allowing capturing the users'
heterogeneity via a finite mixture. We develop a Bayesian Mallows-based finite
mixture model that performs clustering while also accounting for
assessor-related features, called the Bayesian Mallows model with covariates
(BMMx). BMMx is based on a similarity function that a priori favours the
aggregation of assessors into a cluster when their covariates are similar,
using the Product Partition models (PPMx) proposal. We present two approaches
to measure the covariate similarity: one based on a novel deterministic
function measuring the covariates' goodness-of-fit to the cluster, and one
based on an augmented model as in PPMx. We investigate the performance of BMMx
in both simulation experiments and real-data examples, showing the method's
potential for advancing the understanding of assessor preferences and behaviors
in different applications.
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