Amortized Inference for Correlated Discrete Choice Models via Equivariant Neural Networks
This work addresses limitations in capturing realistic substitution patterns in discrete choice models for fields like management science and economics, offering a novel method that improves inference efficiency.
The authors tackled the problem of restrictive assumptions in logit-based discrete choice models by proposing an amortized inference approach using an equivariant neural network emulator to approximate choice probabilities for general error distributions, including correlated errors, resulting in significant gains in accuracy and speed over the GHK simulator in simulations.
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.