Bayesian Plackett--Luce latent block models for ranked data

2026/07/29 by Lapo Santi, Nial Friel, Valeria Vitelli
Mathematics · #stat.ME #stat.AP #stat.CO #msc:62H30 #msc:62F15 #msc:62P10

paper · pdf

53 pages, 12 figures

arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

We introduce a Bayesian latent block model that jointly partitions assessors and items under a Plackett--Luce observation model. Assessors are assigned to C clusters and items to K blocks; items in a block share a common strength parameter within each assessor cluster, yielding a parsimonious C× K co-clustering representation. Independent Gnedin priors infer C and K. Data augmentation gives conjugate Gibbs updates and a tractable MCMC sampler with split-merge moves. Simulations characterize recovery and posterior uncertainty as signal, ranking depth, and group balance vary. Applied to the cancer gene atlas (TCGA) pan-cancer top-500 gene-expression rankings, the model reveals tissue-driven sample structure while compressing gene-level heterogeneity into interpretable blocks. Rank-based GSEA of posterior gene scores supports biological interpretation.

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