Discrete choice models are fundamental tools in management science, economics, and marketing for understanding and predicting decision-making. Logit-based models are dominant in applied work, largely due to their convenient closed-form expressions for choice probabilities. However, these models entail restrictive assumptions on the stochastic utility component, constraining our ability to capture realistic and theoretically grounded choice behavior$-$most notably, substitution patterns. In this work, we propose an amortized inference approach using a neural network emulator to approximate choice probabilities for general error distributions, including those with correlated errors. Our proposal includes a specialized neural network architecture and accompanying training procedures designed to respect the invariance properties of discrete choice models. We provide group-theoretic foundations for the architecture, including a proof of universal approximation given a minimal set of invariant features. Once trained, the emulator enables rapid likelihood evaluation and gradient computation. We use Sobolev training, augmenting the likelihood loss with a gradient-matching penalty so that the emulator learns both choice probabilities and their derivatives. We show that emulator-based maximum likelihood estimators are consistent and asymptotically normal under mild approximation conditions, and we provide sandwich standard errors that remain valid even with imperfect likelihood approximation. Simulations show significant gains over the GHK simulator in accuracy and speed.

翻译：离散选择模型是管理科学、经济学和市场营销中理解与预测决策行为的基础工具。基于Logit的模型因选择概率的封闭形式表达便利而在应用研究中占据主导地位。然而，这类模型对随机效用成分施加了限制性假设，制约了捕捉符合现实与理论基础的决策行为的能力——尤其是替代模式。本文提出一种采用神经网络模拟器的摊销推断方法，以逼近包含相关误差项在内的广义误差分布下的选择概率。我们设计了一种专用神经网络架构及其配套训练流程，旨在保持离散选择模型的不变性特征。我们为该架构提供了群论基础，证明在最小不变特征集约束下可实现通用逼近。训练完成后，该模拟器能快速完成似然评估与梯度计算。我们采用Sobolev训练法，通过梯度匹配惩罚项增强似然损失函数，使模拟器同步学习选择概率及其导数。研究表明，在温和逼近条件下，基于模拟器的最大似然估计量具有一致性与渐进正态性；即便在似然近似不完美时，本文提供的三明治标准误差仍保持有效性。仿真实验表明，该方法在精度与计算速度上均显著优于GHK模拟器。