Entropy-regularized stochastic transport in latent utility space is explored as a tool for behavioral decision modeling under uncertainty in this study, proposing a neural Schrödinger bridge choice model (NSBCM). The NSBCM differs from traditional discrete choice models, which assume that preferences are either latent utilities or random coefficients that are constant across choice contexts. The NSBCM differs from traditional discrete choice models, which assume preferences are either latent utilities or random coefficients fixed across choice contexts. The terminal latent state is then decoded to alternative-specific choice probabilities using an energy-based decoder. The resulting architecture learns the neural drift field, stochastic transport process, and probabilistic choice decoder simultaneously. We test the NSBCM on the publicly available student travel mode choice dataset and benchmark it against the multinomial logit model, the mixed logit model, the neural choice network model, the variational diffusion choice model, and the energy-based preference network model. The proposed model achieves 95.84% accuracy, an F1 score of 0.947, a negative log-likelihood of 0.214, and a Brier score of 0.081. The ablation, transport stability, and contextual perturbation analyses also suggest that Schrödinger transport, entropy regularization, and energy-based decoding contribute to stable and calibrated predictions. The results corroborate the potential of continuous-time latent transport to represent dynamic and heterogeneous choice behavior under uncertainty.
Citation: Irsa Sajjad, Mashail M. Al Sobhi. Neural Schrödinger bridge choice modeling through entropy-regularized stochastic transport of latent behavioral preferences[J]. AIMS Mathematics, 2026, 11(10): 33012-33044. doi: 10.3934/math.20261295
Entropy-regularized stochastic transport in latent utility space is explored as a tool for behavioral decision modeling under uncertainty in this study, proposing a neural Schrödinger bridge choice model (NSBCM). The NSBCM differs from traditional discrete choice models, which assume that preferences are either latent utilities or random coefficients that are constant across choice contexts. The NSBCM differs from traditional discrete choice models, which assume preferences are either latent utilities or random coefficients fixed across choice contexts. The terminal latent state is then decoded to alternative-specific choice probabilities using an energy-based decoder. The resulting architecture learns the neural drift field, stochastic transport process, and probabilistic choice decoder simultaneously. We test the NSBCM on the publicly available student travel mode choice dataset and benchmark it against the multinomial logit model, the mixed logit model, the neural choice network model, the variational diffusion choice model, and the energy-based preference network model. The proposed model achieves 95.84% accuracy, an F1 score of 0.947, a negative log-likelihood of 0.214, and a Brier score of 0.081. The ablation, transport stability, and contextual perturbation analyses also suggest that Schrödinger transport, entropy regularization, and energy-based decoding contribute to stable and calibrated predictions. The results corroborate the potential of continuous-time latent transport to represent dynamic and heterogeneous choice behavior under uncertainty.
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Irsa Sajjad, Mashail M. Al Sobhi. Neural Schrödinger bridge choice modeling through entropy-regularized stochastic transport of latent behavioral preferences[J]. AIMS Mathematics, 2026, 11(10): 33012-33044. doi: 10.3934/math.20261295
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