dorsal/arxiv
View SchemaThe Bayesian Intransitive Bradley-Terry Model via Combinatorial Hodge Theory
| Authors | Hisaya Okahara, Tomoyuki Nakagawa, Shonosuke Sugasawa |
|---|---|
| Categories | |
| ArXiv ID | 2601.07158vv1 |
| URL | https://arxiv.org/abs/2601.07158 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
Pairwise comparison data are widely used to infer latent rankings in areas such as sports, social choice, and machine learning. The Bradley-Terry model provides a foundational probabilistic framework but inherently assumes transitive preferences, explaining all comparisons solely through subject-specific parameters. In many competitive networks, however, cycle-induced effects are intrinsic, and ignoring them can distort both estimation and uncertainty quantification. To address this limitation, we propose a Bayesian extension of the Bradley-Terry model that explicitly separates the transitive and intransitive components. The proposed Bayesian Intransitive Bradley-Terry model embeds combinatorial Hodge theory into a logistic framework, decomposing paired relationships into a gradient flow representing transitive strength and a curl flow capturing cycle-induced structure. We impose global-local shrinkage priors on the curl component, enabling data-adaptive regularization and ensuring a natural reduction to the classical Bradley-Terry model when intransitivity is absent. Posterior inference is performed using an efficient Gibbs sampler, providing scalable computation and full Bayesian uncertainty quantification. Simulation studies demonstrate improved estimation accuracy, well-calibrated uncertainty, and substantial computational advantages over existing Bayesian models for intransitivity. The proposed framework enables uncertainty-aware quantification of intransitivity at both the global and triad levels, while also characterizing cycle-induced competitive advantages among teams.
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"abstract": "Pairwise comparison data are widely used to infer latent rankings in areas such as sports, social choice, and machine learning. The Bradley-Terry model provides a foundational probabilistic framework but inherently assumes transitive preferences, explaining all comparisons solely through subject-specific parameters. In many competitive networks, however, cycle-induced effects are intrinsic, and ignoring them can distort both estimation and uncertainty quantification. To address this limitation, we propose a Bayesian extension of the Bradley-Terry model that explicitly separates the transitive and intransitive components. The proposed Bayesian Intransitive Bradley-Terry model embeds combinatorial Hodge theory into a logistic framework, decomposing paired relationships into a gradient flow representing transitive strength and a curl flow capturing cycle-induced structure. We impose global-local shrinkage priors on the curl component, enabling data-adaptive regularization and ensuring a natural reduction to the classical Bradley-Terry model when intransitivity is absent. Posterior inference is performed using an efficient Gibbs sampler, providing scalable computation and full Bayesian uncertainty quantification. Simulation studies demonstrate improved estimation accuracy, well-calibrated uncertainty, and substantial computational advantages over existing Bayesian models for intransitivity. The proposed framework enables uncertainty-aware quantification of intransitivity at both the global and triad levels, while also characterizing cycle-induced competitive advantages among teams.",
"arxiv_id": "2601.07158",
"authors": [
"Hisaya Okahara",
"Tomoyuki Nakagawa",
"Shonosuke Sugasawa"
],
"categories": [
"stat.ME"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "The Bayesian Intransitive Bradley-Terry Model via Combinatorial Hodge Theory",
"url": "https://arxiv.org/abs/2601.07158",
"version": "v1"
},
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