Covariate Assisted Entity Ranking with Sparse Intrinsic Scores

TL;DR

This paper proposes a new covariate-assisted ranking model that accounts for sparse intrinsic scores, extending the BTL model, with theoretical analysis, estimation methods, and practical validation.

Contribution

It introduces a novel model integrating covariates with sparse intrinsic scores, along with identification conditions, estimation techniques, and goodness-of-fit testing.

Findings

The proposed estimator achieves optimal statistical rates.

The debiased estimator provides valid confidence intervals.

Numerical studies confirm the theoretical properties and effectiveness.

Abstract

This paper addresses the item ranking problem with associate covariates, focusing on scenarios where the preference scores can not be fully explained by covariates, and the remaining intrinsic scores, are sparse. Specifically, we extend the pioneering Bradley-Terry-Luce (BTL) model by incorporating covariate information and considering sparse individual intrinsic scores. Our work introduces novel model identification conditions and examines the regularized penalized Maximum Likelihood Estimator (MLE) statistical rates. We then construct a debiased estimator for the penalized MLE and analyze its distributional properties. Additionally, we apply our method to the goodness-of-fit test for models with no latent intrinsic scores, namely, the covariates fully explaining the preference scores of individual items. We also offer confidence intervals for ranks. Our numerical studies lend further support to our theoretical findings, demonstrating validation for our proposed method