RUMBoost: Gradient Boosted Random Utility Models
Nicolas Salvadé Tim Hillel
This paper introduces the RUMBoost model, a novel discrete choice modelling
approach that combines the interpretability and behavioural robustness of
Random Utility Models (RUMs) with the generalisation and predictive ability of
deep learning methods. We obtain the full functional form of non-linear utility
specifications by replacing each linear parameter in the utility functions of a
RUM with an ensemble of gradient boosted regression trees. This enables
piece-wise constant utility values to be imputed for all alternatives directly
from the data for any possible combination of input variables. We introduce
additional constraints on the ensembles to ensure three crucial features of the
utility specifications: (i) dependency of the utilities of each alternative on
only the attributes of that alternative, (ii) monotonicity of marginal
utilities, and (iii) an intrinsically interpretable functional form, where the
exact response of the model is known throughout the entire input space.
Furthermore, we introduce an optimisation-based smoothing technique that
replaces the piece-wise constant utility values of alternative attributes with
monotonic piece-wise cubic splines to identify non-linear parameters with
defined gradient. We demonstrate the potential of the RUMBoost model compared
to various ML and Random Utility benchmark models for revealed preference mode
choice data from London. The results highlight the great predictive performance
and the direct interpretability of our proposed approach. Furthermore, the
smoothed attribute utility functions allow for the calculation of various
behavioural indicators and marginal utilities. Finally, we demonstrate the
flexibility of our methodology by showing how the RUMBoost model can be
extended to complex model specifications, including attribute interactions,
correlation within alternative error terms and heterogeneity within the
population.