Although the foundations of ranking are well established, the ranking
literature has primarily been focused on simple, unimodal models, e.g. the
Mallows and Plackett-Luce models, that define distributions centered around a
single total ordering. Explicit mixture models have provided some tools for
modelling multimodal ranking data, though learning such models from data is
often difficult. In this work, we contribute a contextual repeated selection
(CRS) model that leverages recent advances in choice modeling to bring a
natural multimodality and richness to the rankings space. We provide rigorous
theoretical guarantees for maximum likelihood estimation under the model
through structure-dependent tail risk and expected risk bounds. As a
by-product, we also furnish the first tight bounds on the expected risk of
maximum likelihood estimators for the multinomial logit (MNL) choice model and
the Plackett-Luce (PL) ranking model, as well as the first tail risk bound on
the PL ranking model. The CRS model significantly outperforms existing methods
for modeling real world ranking data in a variety of settings, from racing to
rank choice voting.

采用基于选择建模的上下文重复选择（CRS）模型，结合多模态模型，提供了生成丰富的排名空间的工具，同时使用结构相关的尾部风险和期望风险界限，对该模型的最大似然估计提供了严格的理论保证，并且在多项式逻辑选择模型（MNL）和 Plackett-Luce（PL）排名模型的预期风险以及 PL 排名模型的尾部风险方面也提供了前所未有的紧密界限。该 CRS 模型在各种场景下明显优于现有的排名数据建模方法，包括比赛和排名投票。

学习丰富排序

Learning Rich Rankings

Choice Modeling is at the core of many economics, operations, and marketing
problems. In this paper, we propose a fundamental characterization of choice
functions that encompasses a wide variety of extant choice models. We
demonstrate how nonparametric estimators like neural nets can easily
approximate such functionals and overcome the curse of dimensionality that is
inherent in the non-parametric estimation of choice functions. We demonstrate
through extensive simulations that our proposed functionals can flexibly
capture underlying consumer behavior in a completely data-driven fashion and
outperform traditional parametric models. As demand settings often exhibit
endogenous features, we extend our framework to incorporate estimation under
endogenous features. Further, we also describe a formal inference procedure to
construct valid confidence intervals on objects of interest like price
elasticity. Finally, to assess the practical applicability of our estimator, we
utilize a real-world dataset from S. Berry, Levinsohn, and Pakes (1995). Our
empirical analysis confirms that the estimator generates realistic and
comparable own- and cross-price elasticities that are consistent with the
observations reported in the existing literature.

本文介绍了一种基于非参数估计的选择模型，该模型使用神经网络逼近各种现有选择模型，并扩展到包括对内生特征的估计，同时介绍了一种有效的置信区间构建方法，使用真实数据进行了实证分析，并验证了其在实际应用中的可行性。

选择模型与置换不变性

Choice Models and Permutation Invariance

The $\texttt{torch-choice}$ is an open-source library for flexible, fast
choice modeling with Python and PyTorch. $\texttt{torch-choice}$ provides a
$\texttt{ChoiceDataset}$ data structure to manage databases flexibly and
memory-efficiently. The paper demonstrates constructing a
$\texttt{ChoiceDataset}$ from databases of various formats and functionalities
of $\texttt{ChoiceDataset}$. The package implements two widely used models,
namely the multinomial logit and nested logit models, and supports
regularization during model estimation. The package incorporates the option to
take advantage of GPUs for estimation, allowing it to scale to massive datasets
while being computationally efficient. Models can be initialized using either
R-style formula strings or Python dictionaries. We conclude with a comparison
of the computational efficiencies of $\texttt{torch-choice}$ and
$\texttt{mlogit}$ in R as (1) the number of observations increases, (2) the
number of covariates increases, and (3) the expansion of item sets. Finally, we
demonstrate the scalability of $\texttt{torch-choice}$ on large-scale datasets.

本文介绍了开源的 $	exttt {torch-choice}$ 库及其数据结构 $	exttt {ChoiceDataset}$ ，实现了两种模型（多项式 Logit 模型和嵌套 Logit 模型）和模型估计中的正则化，支持 R-style 公式字符串或 Python 字典作为模型初始化，GPU 加速可以应对大型数据集，最后与 $	exttt {mlogit}$ 相比较效率更高