# Amortized Inference for Correlated Discrete Choice Models via Equivariant Neural Networks

arXiv: https://arxiv.org/abs/2603.24705 · HTML: https://mlsanity.com/paper/2603.24705/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 59 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Builds on (most cited first, 7 of 7)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Searching for Activation Functions](https://mlsanity.com/paper/1710.05941/) (2017)
- [The Use of Binary Choice Forests to Model and Estimate Discrete Choices](https://mlsanity.com/paper/1908.01109/) (2019)
- [Deep Learning for Choice Modeling](https://mlsanity.com/paper/2208.09325/) (2022)
- [Choice Models and Permutation Invariance: Demand Estimation in Differentiated Products Markets](https://mlsanity.com/paper/2307.07090/) (2023)
- [The generalized stochastic preference choice model](https://mlsanity.com/paper/1803.04244/) (2018)

## Built on by (most cited first, 1 of 1)

- [SAUSS: Stochastic Approximation with Unbiased Simulated Scores for Limited Dependent Variable Models](https://mlsanity.com/paper/2608.25304/) (2026)

## Abstract (arXiv)

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, they impose restrictive assumptions on the stochastic utility component, constraining our ability to capture realistic substitution patterns. We propose an amortized inference approach that relies on a neural network emulator to approximate choice probabilities for general error distributions, including those with correlated errors. We develop a specialized neural network architecture 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 for a psuedo-true parameter even with imperfect likelihood approximation. Simulations show significant gains over the GHK simulator in accuracy and speed.