Amortized Inference for Correlated Discrete Choice Models via Equivariant Neural Networks

arXiv cs.LG / 3/27/2026

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Key Points

The paper addresses limitations of standard logit discrete choice models by introducing an amortized neural-network emulator that can approximate choice probabilities for general—and potentially correlated—error distributions.
It proposes a specialized equivariant architecture grounded in group-theoretic invariance, including a universal approximation result using a minimal set of invariant features.
The approach uses Sobolev training with a gradient-matching penalty, enabling the emulator to learn both choice probabilities and their derivatives to support faster likelihood evaluation and gradient computation.
The authors provide theoretical results showing emulator-based maximum likelihood estimators can be consistent and asymptotically normal under mild approximation assumptions, along with valid “sandwich” standard errors even when approximation is imperfect.
Simulation results indicate improved accuracy and speed versus the GHK simulator, suggesting practical benefits for estimation in discrete choice settings with complex substitution patterns.

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

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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.