Classical latent-score ranking models often fail to distinguish objects' intrinsic scores from contextual effects, which are typically nonlinear and can dominate the observed outcomes. To address this, we introduce a semiparametric ranking framework in which the log-score of each object is modeled as the sum of a utility parameter and a nonparametric covariate effect. Within this framework, we establish model identifiability under mild regularity and connectivity conditions. For estimation, we approximate the covariate effect using a neural network and estimate the parameters via maximum likelihood. Under random design assumptions, we prove that the resulting estimator exists with high probability and derive non-asymptotic error bounds that achieve minimax optimality for both the parametric and nonparametric components. Numerical experiments on both synthetic data and an ATP tennis dataset are conducted to support our findings.

翻译：经典潜在得分排序模型往往难以区分对象的固有得分与情境效应，后者通常具有非线性特征且可能主导观测结果。针对这一问题，我们提出一种半参数排序框架，其中每个对象的对数得分被建模为效用参数与非参数协变量效应之和。在该框架下，我们证明在温和正则性与连通性条件下模型具有可辨识性。在估计方面，我们利用神经网络近似协变量效应，并通过极大似然法估计参数。基于随机设计假设，我们证明了所得估计量以高概率存在，并推导出参数分量与非参数分量均达到极小极大最优性的非渐近误差界。在合成数据与ATP网球数据集上的数值实验验证了我们的理论发现。