Framing Discrete Choice Model as Deep Neural Network with Utility Interpretation

Deep neural network (DNN) has been increasingly applied to travel demand prediction. However, no study has examined how DNN relates to utility-based discrete choice models (DCM) beyond simple comparison of prediction accuracy. To fill this gap, this paper investigates the relationship between DNN and DCM from a theoretical perspective with three major findings. First, we introduce the utility interpretation to the DNN models and demonstrate that DCM is one special case of DNN with shallow and sparse architecture, identifiable parameters, logistic loss, zero regularization, and domain-knowledge based feature transformation. Second, a sequence of four neural network models illustrate how DNN gradually trade away interpretability for predictability in the context of travel mode choice. High predictability is achieved by DNN's powerful representation learning and high model capacity; but interpretability is sacrificed through the loss of convex optimization and statistical properties, and non-identification of parameters. Third, the utility interpretation allows us to develop a numerical method of extracting important economic information from DNN including choice probability, elasticity, marginal rate of substitution, and consumer surplus. Overall, this study makes three contributions: theoretically it frames DCM as a special case of DNN and introduces the utility interpretation to DNN; methodologically it demonstrates the interpretability-predictability tradeoff between DCM and DNN and suggests the potential of their joint improvement, and practically it introduces a post-hoc numerical method to extract economic information from DNN and make it interpretable through the utility concept.