Technology Category
Machine Learning: Probabilistic Circuits and Graphical ModelsSearch and Optimization: Sampling/Simulation-based SearchReasoning under Uncertainty: Probabilistic Inference
Amortized Inference for Correlated Discrete Choice Models via Equivariant Neural Networks
🤖 AI Summary
Traditional logit models struggle to capture correlated choice behavior due to their assumption of independent and identically distributed random utility errors, particularly limiting their ability to model substitution patterns. This work proposes an amortized inference approach based on group-equivariant neural networks that approximates discrete choice probabilities under general error distributions by constructing a neural simulator respecting the model’s invariance structure. Theoretically, the architecture is shown to possess universal approximation capability within the minimal invariant feature set, and Sobolev training is employed to jointly learn choice probabilities and their derivatives. Experiments demonstrate that the method significantly outperforms the GHK simulator in both estimation accuracy and computational efficiency, while the resulting maximum likelihood estimator is proven to be consistent and asymptotically normal.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
discrete choice models
correlated errors
substitution patterns
stochastic utility
choice probabilities
Innovation
Methods, ideas, or system contributions that make the work stand out.
amortized inference
equivariant neural networks
discrete choice models
Sobolev training
universal approximation
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