Ricardo A. Daziano

Siqi Feng, Rui Yao, Stephane Hess et al.

Deep neural networks (DNNs) frequently present behaviorally irregular patterns, significantly limiting their practical potentials and theoretical validity in travel behavior modeling. This study proposes strong and weak behavioral regularities as novel metrics to evaluate the monotonicity of individual demand functions (known as the "law of demand"), and further designs a constrained optimization framework with six gradient regularizers to enhance DNNs' behavioral regularity. The proposed framework is applied to travel survey data from Chicago and London to examine the trade-off between predictive power and behavioral regularity for large vs. small sample scenarios and in-domain vs. out-of-domain generalizations. The results demonstrate that, unlike models with strong behavioral foundations such as the multinomial logit, the benchmark DNNs cannot guarantee behavioral regularity. However, gradient regularization (GR) increases DNNs' behavioral regularity by around 6 percentage points (pp) while retaining their relatively high predictive power. In the small sample scenario, GR is more effective than in the large sample scenario, simultaneously improving behavioral regularity by about 20 pp and log-likelihood by around 1.7%. Comparing with the in-domain generalization of DNNs, GR works more effectively in out-of-domain generalization: it drastically improves the behavioral regularity of poorly performing benchmark DNNs by around 65 pp, indicating the criticality of behavioral regularization for enhancing model transferability and application in forecasting. Moreover, the proposed framework is applicable to other NN-based choice models such as TasteNets. Future studies could use behavioral regularity as a metric along with log-likelihood in evaluating travel demand models, and investigate other methods to further enhance behavioral regularity when adopting complex machine learning models.

Daniel F. Villarraga, Ricardo A. Daziano

We introduce a novel model architecture that incorporates network effects into discrete choice problems, achieving higher predictive performance than standard discrete choice models while offering greater interpretability than general-purpose flexible model classes. Econometric discrete choice models aid in studying individual decision-making, where agents select the option with the highest reward from a discrete set of alternatives. Intuitively, the utility an individual derives from a particular choice depends on their personal preferences and characteristics, the attributes of the alternative, and the value their peers assign to that alternative or their previous choices. However, most applications ignore peer influence, and models that do consider peer or network effects often lack the flexibility and predictive performance of recently developed approaches to discrete choice, such as deep learning. We propose a novel graph convolutional neural network architecture to model network effects in discrete choices, achieving higher predictive performance than standard discrete choice models while retaining the interpretability necessary for inference--a quality often lacking in general-purpose deep learning architectures. We evaluate our architecture using revealed commuting choice data, extended with travel times and trip costs for each travel mode for work-related trips in New York City, as well as 2016 U.S. election data aggregated by county, to test its performance on datasets with highly imbalanced classes. Given the interpretability of our models, we can estimate relevant economic metrics, such as the value of travel time savings in New York City. Finally, we compare the predictive performance and behavioral insights from our architecture to those derived from traditional discrete choice and general-purpose deep learning models.

Prateek Bansal, Rico Krueger, Michel Bierlaire et al.

The standard Gibbs sampler of Mixed Multinomial Logit (MMNL) models involves sampling from conditional densities of utility parameters using Metropolis-Hastings (MH) algorithm due to unavailability of conjugate prior for logit kernel. To address this non-conjugacy concern, we propose the application of Pólygamma data augmentation (PG-DA) technique for the MMNL estimation. The posterior estimates of the augmented and the default Gibbs sampler are similar for two-alternative scenario (binary choice), but we encounter empirical identification issues in the case of more alternatives ($J \geq 3$).

Prateek Bansal, Rico Krueger, Michel Bierlaire et al.

Variational Bayes (VB) methods have emerged as a fast and computationally-efficient alternative to Markov chain Monte Carlo (MCMC) methods for scalable Bayesian estimation of mixed multinomial logit (MMNL) models. It has been established that VB is substantially faster than MCMC at practically no compromises in predictive accuracy. In this paper, we address two critical gaps concerning the usage and understanding of VB for MMNL. First, extant VB methods are limited to utility specifications involving only individual-specific taste parameters. Second, the finite-sample properties of VB estimators and the relative performance of VB, MCMC and maximum simulated likelihood estimation (MSLE) are not known. To address the former, this study extends several VB methods for MMNL to admit utility specifications including both fixed and random utility parameters. To address the latter, we conduct an extensive simulation-based evaluation to benchmark the extended VB methods against MCMC and MSLE in terms of estimation times, parameter recovery and predictive accuracy. The results suggest that all VB variants with the exception of the ones relying on an alternative variational lower bound constructed with the help of the modified Jensen's inequality perform as well as MCMC and MSLE at prediction and parameter recovery. In particular, VB with nonconjugate variational message passing and the delta-method (VB-NCVMP-Delta) is up to 16 times faster than MCMC and MSLE. Thus, VB-NCVMP-Delta can be an attractive alternative to MCMC and MSLE for fast, scalable and accurate estimation of MMNL models.