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Neural-Bayesian Structure Learning for Discrete Choice Modeling
Hyunsoo Yun, Eun Hak Lee, Jiaru Zhang, Ziran Wang, Eui-Jin Kim
TL;DR
Conventional discrete-choice and machine-learning models lack an internal representation of how related attributes adjust when one is deliberately changed. Neural-BSL jointly learns attribute dependencies and a random-utility choice model, and finds that propagating interventions can alter predicted mode redistribution while revealing downstream traveler and trip adjustments.
Problem
Existing mode-choice methods do not represent how explanatory variables relate structurally, limiting their treatment of deliberate attribute changes.
Method
Neural-BSL jointly performs differentiable Bayesian structure learning and random-utility discrete-choice estimation in one procedure.
Results
Propagating interventions through learned dependencies changes predicted mode redistribution and exposes downstream traveler and trip adjustments across policy scenarios.
Takeaways & Limitations
Learned dependency structures provide a basis for evaluating mode-share responses together with associated downstream attribute changes.
Takeaways & Limitations
Cross-sectional analysis leaves directional ambiguities, while the method’s causal interpretation relies on a standard assumption.
Abstract
from arXiv · showhide
Conventional discrete choice and machine learning models are estimated primarily from observational data and typically treat explanatory covariates as parallel inputs, providing no internal mechanism for determining how related attributes should adjust when one is deliberately changed. This paper proposes Neural-Bayesian Structure Learning (Neural-BSL), a framework coupling differentiable structure learning with random-utility-based discrete choice estimation in a single differentiable procedure. To prevent mutually exclusive choice outcome from distorting the recovered attribute structure, the observed choice is maintained outside the graph as an alternative-specific utility comparison, while the attribute structure and random-utility parameters are learned jointly. The learned structure enters the choice model through structure-weighted attribute interactions and provides the structural basis for propagating interventions through downstream attributes. An intervention is evaluated by updating the intervened attribute, propagating its model-implied downstream changes in topological order, and then recomputing utilities and choice probabilities. This yields both predicted mode-share responses and the associated changes in downstream traveler or trip attributes. We evaluate Neural-BSL using stated-preference data from Seoul and the revealed-preference data from London. Neural-BSL achieves predictive performance comparable to conventional benchmarks while recovering behaviorally coherent dependency structures. Across policy scenarios, propagating interventions through the learned structure changes the predicted redistribution across modes while exposing the downstream traveler and trip adjustments underlying those responses.
1. Introduction
Neural-BSL addresses the gap between predictive mode-choice modeling and interventional policy analysis by jointly learning directed attribute dependencies and a random-utility choice model. Its structural simulations propagate interventions through downstream attributes, producing mode-share forecasts alongside the traveler or trip adjustments underlying them.
- Motivation: Conventional choice and machine-learning models do not identify how related attributes adjust when one explanatory variable is deliberately changed.They represent covariates as parallel inputs or quantify predictive contributions under the data-generating distribution, without an interventional operation for remaining inputs.
- Framework: Neural-BSL keeps observed choice outside the learned attribute graph as an alternative-specific utility comparison while learning dependencies over explanatory attributes.This preserves the observed choice outcome for random-utility estimation while preventing mutually exclusive choice outcomes from distorting the recovered attribute structure.
- Contribution: Neural-BSL combines structure learning and discrete choice modeling in a single end-to-end differentiable estimation procedure grounded in random utility theory.The discovered directed dependency structure and fitted choice model inform one another rather than being estimated independently.
- Choice specification: The discovered structure participates directly in the fitted choice model through a utility specification with individual-level LOS coefficients and ASCs dependent on that structure.The structure is therefore not merely a separate descriptive output.
- Policy simulation: Structural policy simulations propagate interventions through downstream attributes and report both mode-share changes and accompanying traveler or trip adjustments.This allows the structural response underlying each forecast to be examined explicitly.
2. Related work
Related work shows that conventional choice models retain behavioral interpretability but require analyst-specified nonlinearities and attribute structures, while machine-learning and hybrid models do not recover dependencies for intervention propagation. Differentiable structure learning provides a compatible basis for jointly learning variable dependencies and discrete choice models, yet no existing framework unifies these tasks.
- Conventional choice models: Conventional discrete choice models provide behaviorally meaningful coefficients but require analysts to specify nonlinearities, interactions, taste distributions, and structural paths in advance.MNL, nested logit, mixed logit, and ICLV models extend random-utility choice analysis while retaining analyst-specified structures.
- Conventional choice models: Conventional specifications treat observed individual attributes as parallel utility inputs, leaving no internal mechanism to adjust downstream attributes after upstream intervention.Examples include vehicle ownership depending on income and license holding depending on age, relationships that are not learned from the data.
- Machine-learning choice models: Machine-learning models capture nonlinearities and interactions and can match or exceed MNL predictive accuracy, but their attributions describe observed associations rather than behavioral intervention mechanisms.Tree ensembles and MLPs improve flexibility, while importance measures such as SHAP explain predictions post hoc.
- Hybrid neural-utility models: Hybrid neural-utility models preserve random-utility choice structure by learning utility terms or taste parameters with neural networks, but still lack structural relationships among explanatory variables.L-MNL, TasteNet-MNL, and ResLogit recover some interpretability while treating characteristics as parallel inputs rather than upstream and downstream attributes.
- Differentiable structure learning: Differentiable structure learning replaces combinatorial graph search with gradient-based optimization, making dependency recovery compatible with gradient-based choice-model estimation.NOTEARS and DiBS motivate a smooth graph representation, while causal modeling distinguishes recovering structure from estimating intervention effects.
- Research gap: No existing framework recovers dependencies among individual attributes and estimates a discrete choice model within one differentiable procedure.This gap motivates a unified approach linking directed dependency learning with discrete choice estimation.
3. Dataset
The study evaluates Neural-BSL on complementary stated-preference data from Seoul and revealed-preference data from London, spanning controlled choice experiments and real-world network conditions. The datasets differ in scale, geography, elicitation method, and attribute construction while sharing preprocessing before framework estimation.
- Dataset overview: The analysis combines a Seoul stated-preference survey with London’s revealed-preference LPMC benchmark to evaluate the framework across distinct data-generating environments.Seoul provides designed choice experiments with exogenously assigned LOS attributes, while London provides large-scale revealed behavior with observed network-derived supply conditions.
- Seoul SP dataset: The Seoul SP dataset contains 863 respondents completing six tasks each, yielding 5,178 observations across bus, subway, and demand-responsive transit.The D-efficient scenarios vary five LOS attributes, with eleven varying mode-specific LOS attributes retained in the utility specification after excluding designed constants.
- London LPMC dataset: The London LPMC dataset contains 81,086 trips from 31,954 individuals across 17,616 households, with walking, cycling, public transport, and driving as alternatives.Mode shares are 17.6% walking, 3.0% cycling, 35.3% public transport, and 44.2% driving.
- Common preprocessing: Both datasets use training-only standardization for utility attributes, while structural scores preserve binary indicators at 0/1 and standardize continuous attributes.Choices are encoded as integer labels for multinomial negative log-likelihood evaluation, and the LPMC split is grouped by household to prevent intra-household leakage.
4. Methodology
Neural-BSL jointly learns a posterior over attribute dependency graphs and a discrete-choice model while keeping the observed choice outside the attribute DAG. The learned structure enters utilities through weighted attribute interactions and supports intervention propagation to downstream attributes, choice probabilities, and other attributes.
- Framework overview: The observed choice is excluded from the attribute DAG, while structure learning, structure-weighted interactions, and interventions operate on the graph over individual attributes.Alternative-specific level-of-service attributes enter utility directly without passing through the attribute graph.
- Framework overview: Neural-BSL recovers directional dependencies among individual attributes and estimates utilities that reflect the discovered structure, allowing interventions to affect choices and other attributes.The framework’s objective combines structure recovery with a choice model whose individual-level utility is conditional on that structure.
- Framework overview: The framework has three blocks: differentiable structure learning, structure-weighted utility specification, and discrete choice with softmax probabilities.The utility block pairs each attribute with a weighted sum of its parents, while separate networks produce level-of-service coefficients and alternative-specific constants.
- Differentiable structure learning: Differentiable Bayesian structure learning represents edge probabilities with soft adjacency matrices and particle-based posterior approximations over DAGs.Continuous latent embeddings enable gradient-based graph optimization, while maintaining a posterior distribution captures structural uncertainty from limited observational information.
- Joint training and intervention: The choice and structural losses are coupled through graph and structural-coefficient parameters in a single objective, so both shape the posterior over structural parameters.This coupling preserves the joint differentiability linking structure learning and choice estimation.
5. Results
Neural-BSL matches conventional models in predictive accuracy while recovering behaviorally coherent dependency structures and theoretically consistent attribute effects. Its learned structure changes intervention-based mode-share responses by propagating downstream adjustments through traveler and trip attributes.
- Predictive performance: Mean accuracies remain within narrow dataset-specific bands, with MLP highest on both datasets and Neural-BSL at 0.742 on RP.On SP, MNL and MLP range from 0.583 to 0.593; on RP, they range from 0.740 to 0.746.
- Behavioral coherence: All eleven Neural-BSL own-effects on both datasets have theoretically expected non-positive signs, and mean utility coefficients agree in sign in every case.The results indicate sign consistency for both own-effects and mean utility coefficients.
- Recovered structure: The learned graphs replace hand-specified ordering with data-driven directed dependencies jointly optimized with utility coefficients, linking traveler attributes through recurring structural pathways.The recovered relationships connect socioeconomic characteristics, license possession, car ownership, mobility resources, and trip-context variables.
- Downstream contributions: Direct contributions exceed summed downstream contributions for every source attribute, while downstream channels remain behaviorally meaningful for license possession, age, and commute context.The largest reported downstream-to-direct ratios are 28.7% for license possession in SP and 13.9% for age in RP.
- SP interventions: In SP, license surrender among license holders aged 50 or above reduces DRT by 0.99 pp under Neural-BSL versus 0.64 pp under MNL, while subway rises 0.53 pp instead of falling 0.23 pp.The learned license-to-car pathway propagates lost private-vehicle availability into a different substitution pattern across transit modes.
6. Conclusions and future work
Neural-BSL jointly learns traveler-attribute dependencies and a discrete choice model, then propagates interventions through the learned structure to explain both mode-share changes and downstream attribute adjustments. Results show behaviorally meaningful mediation and direction-dependent mode shifts, while limitations concern causal sufficiency, structural-learning choices, cross-sectional data, respondent-profile counts, and excluded endogenous level-of-service attributes.
- Core framework: Neural-BSL jointly estimates a differentiable traveler-attribute dependency structure and a random-utility choice model, rather than learning them in disconnected stages.The observed choice remains outside the DAG, while structure-weighted attribute interactions enter the choice model.
- Core framework: Intervention analysis propagates exogenous changes through the learned DAG before recomputing choice probabilities, revealing mode-share responses and downstream traveler or trip adjustments.This extends beyond static ceteris paribus simulations that change only the target covariate.
- Empirical findings: The empirical analysis used stated-preference data from Seoul and revealed-preference data from London, with structures learned from data rather than fixed in advance.The fitted model separates direct utility contributions from additional effects associated with downstream structural relationships.
- Empirical findings: Downstream channels captured behaviorally meaningful mediation for license possession, age, and commute context, while intervention-target position determined which attributes could adjust.These adjustments could strengthen, moderate, redistribute, or reverse predicted mode shifts, including the observed SP subway response.
- Limitations: The framework’s causal interpretation assumes causal sufficiency, and its learned DAG depends on regularization, edge-retention criteria, prior masks, and cross-sectional observational information.Unmeasured confounding is not addressed, and alternative structural-learning settings may alter edges and downstream interpretations.
Appendix A. Attitudinal items and factor analysis
Appendix A reduces 17 stated-preference attitudinal items to four factor-score attributes for Neural-BSL using leakage-controlled exploratory factor analysis, with adequate sampling diagnostics and 37.3% cumulative variance explained.
- Factor construction: Seventeen Likert-scale items are reduced to four continuous factor scores for use as Neural-BSL attitudinal attributes instead of raw items.All 17 items are retained without ex-ante exclusion.
- Factor construction: Exploratory factor analysis uses minimum-residual extraction with varimax rotation and is fitted only on 604 training respondents to prevent partition leakage.Validation and test respondents are excluded from factor fitting.
- Factor construction: The four constructs are punctuality, efficiency, comfort, and innovativeness.These constructs were grouped a priori.
- Diagnostics: The overall KMO measure is 0.82, with every per-item KMO at least 0.51, indicating satisfactory sampling adequacy.The reported KMO diagnostics support proceeding with factor analysis.
- Diagnostics: Bartlett’s test rejects an identity correlation matrix (χ² = 2,384.27, df = 136, p < 0.001), while four factors explain 37.3% of total item variance.Together, these results support factor-analysis appropriateness and summarize the extracted solution’s variance coverage.
Appendix B. Causal plausibility mask
The appendix introduces a causal plausibility mask to address ambiguities and implausible directions in purely data-driven structure learning. It excludes directions inconsistent with temporal ordering, variable construction, or application-specific interpretation while leaving the remaining directions data-learned.
- Motivation: Observational data may not identify edge directions because multiple DAGs can belong to the same Markov equivalence class.Strong or nearly deterministic associations can also favor directions that are difficult to justify using temporal or substantive knowledge.
- Mask construction: The mask excludes directions that are difficult to support given temporal ordering, variable construction, or the interpretation adopted in the application.This addresses cases such as predicting license possession from car ownership despite license holding generally preceding vehicle acquisition.
- Mask construction: All directions remaining after masking are left for the model to learn from the data.
SP Dataset mask
The SP dataset mask applies six rules to the 17-attribute DAG, constraining parent relationships according to exogeneity, life-course ordering, causal precedence, and variable construction.
- SP Dataset mask: Six rules constrain the parent relationships among the 17 attributes in the SP DAG.The rules define the dataset-specific structure mask.
- SP Dataset mask: Gender and age cohort are exogenous with no parents, while education may have only gender and age cohort as parents.Education’s allowed parents reflect its earlier position in the life course.
- SP Dataset mask: Car ownership cannot parent license holding or income, because license acquisition precedes ownership and income is the upstream socioeconomic resource.These constraints encode temporal and socioeconomic ordering in the cross-sectional specification.
- SP Dataset mask: The long-commute indicator cannot parent transfer count because transfer requirements contribute to commute duration.This rule treats transfer requirements as conditions contributing to commute duration.
- SP Dataset mask: The two occupation indicators cannot parent each other because both derive from the same categorical occupation variable.Their mutual exclusion reflects shared source-variable construction.
RP Dataset mask
The RP dataset contains 11 attributes divided into six person-level and five trip-context attributes, with five rules constraining their allowable dependency structure. These rules encode exogeneity, temporal ordering, and mutual exclusivity assumptions.
- Dataset composition: The RP dataset includes 11 attributes: six person-level attributes and five trip-context attributes, governed by five dependency-structure rules.The rules constrain which attributes may have parents in the learned structure.
- Exogeneity and temporal ordering: Female, age, weekend, and winter-month indicators are exogenous and therefore have no parents.These four indicators are treated as exogenous variables in the RP dataset.
- Exogeneity and temporal ordering: Trip-context attributes cannot parent license holding, car availability, or fare-concession status, which precede the observed trip.These attributes are treated as established before the observed trip.
- Exogeneity and temporal ordering: Car availability cannot parent license holding because license acquisition precedes access to a household car.The rule imposes a temporal ordering between license holding and car availability.
- Exogeneity and temporal ordering: Rush-hour travel cannot parent commute status, while age-based and disability-based fare-concession indicators cannot parent each other because they are mutually exclusive categories.Trip purpose precedes commute status, and both concession indicators derive from the same fare-type variable.
Appendix C. Benchmark specifications and sensitivity analysis · C.1 Specification-matched MNL
The specification-matched MNL mirrors Neural-BSL’s initialized linear utility specification and supplies warm-start coefficients, while Neural-BSL adds graph-dependent and nonlinear components. A sensitivity analysis highlights how sign constraints alter the estimated rail-duration effect under collinearity.
- C.1 Specification-matched MNL: The MNL benchmark matches Neural-BSL’s initialization specification, including LOS coefficients, ASCs, mode-specific individual-attribute coefficients, and LOS-by-individual interactions.Parameters are estimated by maximum likelihood with L2-regularized interaction terms.
- C.1 Specification-matched MNL: Fitted MNL coefficients warm-start Neural-BSL’s corresponding linear utility components, while graph-dependent and nonlinear components begin at small magnitude.This initializes Neural-BSL near the specification-matched MNL solution.
- C.1 Specification-matched MNL: Tables C.1 and C.2 report LOS coefficients, ASCs, and mode-specific individual-attribute coefficients for the SP and RP datasets.LOS-by-individual and pairwise interaction terms are included but not tabulated.
- C.1 Specification-matched MNL: The reference mode is bus for SP and walk for RP.Coefficients are reported without standard errors because L2-regularized interaction terms make conventional unpenalized maximum-likelihood standard errors inapplicable.
- C.1 Specification-matched MNL: The RP public-transport duration components are highly collinear, and specification-matched MNL estimates rail duration at +0.031.The positive estimate contrasts with Neural-BSL’s sign-constrained estimate for the same variable.
- C.1 Specification-matched MNL: Neural-BSL’s sign penalty yields a negative mean rail-duration coefficient of −0.211.Rail duration is unchanged in Section 5.4 scenarios, while fare scenarios modify only corresponding fare terms.
C.2 MLP hyperparameter tuning
The MLP benchmark is tuned by refitting twelve architecture and regularization configurations across five cross-validation folds and selecting the highest mean log-likelihood. The selected SP and RP models each use one hidden layer with dropout 0.2 but differ in width, learning rate, weight decay, and achieved log-likelihood.
- Tuning procedure: The MLP benchmark searches twelve configurations varying hidden-layer number and width, dropout, and L2 weight decay at a fixed learning rate.Each configuration is refit on the same five cross-validation folds used for the other models, and the highest mean log-likelihood is reported.
- Selected configurations: On SP data, the selected MLP has one 16-unit hidden layer, dropout 0.2, learning rate 3e-3, weight decay 1e-2, and mean log-likelihood −0.898.The model uses the same input vector as the MNL and Neural-BSL specifications.
- Selected configurations: On RP data, the selected MLP has one 64-unit hidden layer, dropout 0.2, learning rate 1e-3, weight decay 1e-4, and mean log-likelihood −0.659.The selected RP configuration differs from SP primarily in hidden-layer width, learning rate, and weight decay.
C.3 Sensitivity analysis
The sensitivity analysis re-estimates Neural-BSL across dataset-specific structural-loss-weight grids and evaluates predictive, structural, and acyclicity outcomes across candidate values.
- C.3 Sensitivity analysis: Neural-BSL is re-estimated over three candidate structural-loss weights for each dataset, using {1 × 10^-3, 1 × 10^-2, 5 × 10^-2} on SP and {1 × 10^-4, 1 × 10^-3, 1 × 10^-2} on RP.The grids differ because structural and choice losses have different scales across the two datasets.
- C.3 Sensitivity analysis: Figure C.2 reports test accuracy, held-out structural log-likelihood, and acyclicity violation across the candidate structural-loss weights for SP and RP.Held-out structural log-likelihood is averaged over five folds.