Representing Random Utility Choice Models with Neural Networks
This provides a new method for discrete choice modeling, which is incremental as it adapts deep learning to an existing framework.
The paper tackles the problem of modeling discrete choices by proposing RUMnets, a neural network-based class of models inspired by random utility maximization, showing they can approximate any RUM model arbitrarily closely and achieve competitive predictive accuracy on real-world datasets.
Motivated by the successes of deep learning, we propose a class of neural network-based discrete choice models, called RUMnets, inspired by the random utility maximization (RUM) framework. This model formulates the agents' random utility function using a sample average approximation. We show that RUMnets sharply approximate the class of RUM discrete choice models: any model derived from random utility maximization has choice probabilities that can be approximated arbitrarily closely by a RUMnet. Reciprocally, any RUMnet is consistent with the RUM principle. We derive an upper bound on the generalization error of RUMnets fitted on choice data, and gain theoretical insights on their ability to predict choices on new, unseen data depending on critical parameters of the dataset and architecture. By leveraging open-source libraries for neural networks, we find that RUMnets are competitive against several choice modeling and machine learning methods in terms of predictive accuracy on two real-world datasets.