Alternative Graph Neural Networks: Synergizing GEV Models and Deep Learning for Travel Mode Choice Modeling
Authors: Yuqi Zhou, Zhanhong Cheng, Dingyi Zhuang, Lingqian Hu, Yuheng Bu, Shenhao Wang
Organizations: aDepartment of Urban and Regional Planning, University of Florida · dDepartment of Civil and Environmental Engineering, Massachusetts Institute of Technology · bCollege of Architecture, Texas A&M University · cDepartment of Computer Science, University of California, Santa Barbara
Abstract
Generalized extreme value models capture dependence among choice alternatives in discrete choice modeling, but require this dependence to be predefined, symmetric, and shared uniformly across individuals. Recent efforts to synergize discrete choice models with deep neural networks have improved predictive performance but still cannot explicitly represent alternative dependence within neural architectures. To address these gaps, we introduce the alternative graph -- a graph in which nodes represent choice alternatives and edges encode their dependence -- and propose Alternative Graph Neural Networks (Alt-GNNs), a family of GNN-based discrete choice models that embed alternative dependence within a unified framework. Theoretically, Alt-GNNs incorporate multinomial logit, nested logit, and ASU-DNN as special cases and enable innovative model designs, including Nested Alt-GNN, Complete Alt-GNN, and Attention Alt-GNN. Alt-GNNs are consistent with random utility maximization theory, enforce behavioral constraints through alternative graphs, and offer a novel graph-based interpretation of utility functions. Empirically, on two travel mode choice datasets from London and Chicago, Alt-GNNs significantly improve predictive performance over all benchmark models in mode choice modeling because of their flexible alternative graph design and vast hyperparameter space. Even the simplest Alt-GNN variant -- Nested Alt-GNN -- generalizes the nested logit model while preserving its unique two-layer substitution properties, enabling graph-based behavioral constraints over otherwise unconstrained behavioral patterns from deep neural networks.
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.
Discrete choice models (DCMs) are used to analyze individual decision-making in contexts such as transportation choices, political elections, and consumer preferences. DCMs play a central role in applied econometrics by enabling inference on key economic variables, such as marginal rates of substitution, rather than focusing solely on predicting choices on new unlabeled data. However, while traditional DCMs offer high interpretability and support for point and interval estimation of economic quantities, these models often underperform in predictive tasks compared to deep learning (DL) models. Despite their predictive advantages, DL models remain largely underutilized in discrete choice due to concerns about their lack of interpretability, unstable parameter estimates, and the absence of established methods for uncertainty quantification. Here, we introduce a deep learning model architecture specifically designed to integrate with approximate Bayesian inference methods, such as Stochastic Gradient Langevin Dynamics (SGLD). Our proposed model collapses to behaviorally informed hypotheses when data is limited, mitigating overfitting and instability in underspecified settings while retaining the flexibility to capture complex nonlinear relationships when sufficient data is available. We demonstrate our approach using SGLD through a Monte Carlo simulation study, evaluating both predictive metrics--such as out-of-sample balanced accuracy--and inferential metrics--such as empirical coverage for marginal rates of substitution interval estimates. Additionally, we present results from two empirical case studies: one using revealed mode choice data in NYC, and the other based on the widely used Swiss train choice stated preference data.
We introduce, to our knowledge, the first deep generative modeling framework for probability distributions continuously supported on compact metric graphs. Given source and target measures on a metric graph, our method embeds the graph into a smooth ambient space, solves an entropic Kantorovich problem via a neural semidual parameterization, and projects generated samples back onto the original graph. We study two embedded geometries: an extrinsic Euclidean realization and the intrinsic tropical Abel--Jacobi embedding into the Jacobian torus. In both cases, the resulting generator is graph-supported by construction. We prove that, in the joint limit of increasing neural expressivity, the learned generator converges weakly to a valid transport coupling between the original graph measures. Empirically, across a range of geometrically distinct graphs, our method matches or improves upon heuristic transport baselines based on discrete graph OT, while scaling more favorably. Finally, we demonstrate scalability on real-world urban mobility data by training our model on one million Uber pickup locations in Manhattan, New York City.