Core Concepts
Efficiently estimating rankings with covariate information using a novel maximum likelihood estimator.
Abstract
The content delves into the statistical estimation and inference for ranking problems incorporating covariate information. It introduces the Covariate-Assisted Ranking Estimation (CARE) model, extending the Bradley-Terry-Luce model. The paper discusses identifiability conditions, statistical rates for Maximum Likelihood Estimator (MLE), asymptotic distribution, and uncertainty quantification through large-scale numerical studies. Key challenges include feature incorporation, identifiability issues, and quantifying uncertainty in high-dimensional inference.
Introduction to Ranking Problems: Discusses the significance of rankings in various fields.
Bradley-Terry-Luce Model: Introduces the traditional model for ranking problems.
Incorporating Covariates: Explores the need to include covariate information in ranking models.
Challenges in Statistical Inference: Addresses challenges in statistical inference for the CARE model.
Maximum Likelihood Estimator: Introduces a novel MLE for estimating intrinsic scores and covariate effects.
Rate of Convergence: Discusses the statistical consistency results for MLE under specific assumptions.
Uncertainty Quantification: Details methods to quantify uncertainty in MLE through approximation errors and asymptotic distributions.
Comparison with Prior Literature: Contrasts findings with existing works on ranking models without covariates.
Stats
np > cp log n for some cp > 0
L ≤ c4 * nc5 for any absolute constants c4, c5 > 0
Quotes
"Can one design a provably efficient mechanism for ranking by incorporating features of compared items?" - Jianqing Fan