High-dimensional covariate-assisted ranking
Abstract
Ranking data in modern applications often involves covariate vectors whose dimension grows with the number of objects. Identifying relevant covariates and integrating them with item-specific utilities can yield better predictive performance. In this work, we study a Plackett--Luce model that incorporates both item-specific utilities and high-dimensional covariate effects. Under a sparsity assumption on the covariate coefficients, we establish a necessary and sufficient condition for identifiability in terms of the Kruskal rank of the restricted covariate design. We then propose an ℓ1-regularized maximum likelihood estimator for the covariate coefficients. Under suitable design and connectivity conditions, we establish the existence and uniqueness of the estimator with probability tending to one, as well as its uniform consistency. With an additional minimum-signal condition, we further establish exact support recovery. Our analysis combines a hypergraph-based chaining technique with a profile-likelihood perturbation analysis, yielding estimation rates that explicitly capture the effects of the comparison hypergraph's connectivity and the underlying sparsity level. Numerical experiments using synthetic data and a horse racing dataset corroborate our theoretical findings.
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BibTeX
@misc{liu2026highdimensional,
title = {{High-dimensional covariate-assisted ranking}},
author = {Yujia Liu and Yuanyuan Lin and Ruijian Han and Yiming Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26796},
eprint = {2610.26796},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26796},
}
RIS
TY - UNPB
TI - High-dimensional covariate-assisted ranking
AU - Yujia Liu
AU - Yuanyuan Lin
AU - Ruijian Han
AU - Yiming Xu
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26796
UR - https://arxiv.org/abs/2610.26796
AB - Ranking data in modern applications often involves covariate vectors whose dimension grows with the number of objects. Identifying relevant covariates and integrating them with item-specific utilities can yield better predictive performance. In this work, we study a Plackett--Luce model that incorporates both item-specific utilities and high-dimensional covariate effects. Under a sparsity assumption on the covariate coefficients, we establish a necessary and sufficient condition for identifiability in terms of the Kruskal rank of the restricted covariate design. We then propose an ℓ_1-regularized maximum likelihood estimator for the covariate coefficients. Under suitable design and connectivity conditions, we establish the existence and uniqueness of the estimator with probability tending to one, as well as its uniform consistency. With an additional minimum-signal condition, we further establish exact support recovery. Our analysis combines a hypergraph-based chaining technique with a profile-likelihood perturbation analysis, yielding estimation rates that explicitly capture the effects of the comparison hypergraph's connectivity and the underlying sparsity level. Numerical experiments using synthetic data and a horse racing dataset corroborate our theoretical findings.
ER -