# Bayesian Deep Learning for Discrete Choice

arXiv: https://arxiv.org/abs/2505.18077 · HTML: https://mlsanity.com/paper/2505.18077/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 17 of 17)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [The Case for Bayesian Deep Learning](https://mlsanity.com/paper/2001.10995/) (2020)
- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [A Neural-embedded Choice Model: TasteNet-MNL Modeling Taste Heterogeneity with Flexibility and Interpretability](https://mlsanity.com/paper/2002.00922/) (2020)
- [Theory-based residual neural networks: A synergy of discrete choice models and deep neural networks](https://mlsanity.com/paper/2010.11644/) (2020)
- [Combining Discrete Choice Models and Neural Networks through Embeddings: Formulation, Interpretability and Performance](https://mlsanity.com/paper/2109.12042/) (2021)
- [Deep neural networks for choice analysis: Enhancing behavioral regularity with gradient regularization](https://mlsanity.com/paper/2404.14701/) (2024)
- [Designing Graph Convolutional Neural Networks for Discrete Choice with Network Effects](https://mlsanity.com/paper/2503.09786/) (2025)
- [Incorporating uncertainty quantification into travel mode choice modeling: a Bayesian neural network (BNN) approach and an uncertainty-guided active survey framework](https://mlsanity.com/paper/2406.10948/) (2024)
- [Cooperative Variance Estimation and Bayesian Neural Networks for Disentangling Aleatoric and Epistemic Uncertainties](https://mlsanity.com/paper/2505.02743/) (2025)

## Abstract (arXiv)

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.