Amortized Inference for Correlated Discrete Choice Models via Equivariant Neural Networks

Easton K. Huch and Michael Keane

No 35037, NBER Working Papers from National Bureau of Economic Research, Inc

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.

JEL-codes: C10 C13 C15 C25 C35 C45 (search for similar items in EconPapers)
Date: 2026-04
New Economics Papers: this item is included in nep-cmp, nep-dcm and nep-upt
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Working Paper: Amortized Inference for Correlated Discrete Choice Models via Equivariant Neural Networks (2026)
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