Amortized Inference for Correlated Discrete Choice Models via Equivariant Neural Networks

TL;DR

This paper introduces a neural network-based emulator for discrete choice models that captures correlated errors and complex substitution patterns, enabling fast, accurate likelihood evaluation and inference.

Contribution

It develops a specialized neural network architecture with invariance properties for approximating choice probabilities in complex discrete choice models, including correlated errors.

Findings

The emulator achieves higher accuracy and speed than traditional GHK simulation.

Maximum likelihood estimators based on the emulator are consistent and asymptotically normal.

The approach allows rapid likelihood evaluation and gradient computation for complex models.

Abstract

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.