# RUMBoost: Gradient Boosted Random Utility Models

arXiv: https://arxiv.org/abs/2401.11954 · HTML: https://mlsanity.com/paper/2401.11954/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 38 references that are in the map.
- First posted on arXiv 22 Jan 2024.

## Builds on (most cited first, 7 of 7)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [A Neural-embedded Choice Model: TasteNet-MNL Modeling Taste Heterogeneity with Flexibility and Interpretability](https://mlsanity.com/paper/2002.00922/) (2020)
- [Consistent feature attribution for tree ensembles](https://mlsanity.com/paper/1706.06060/) (2017)
- [A Comparative study of Hyper-Parameter Optimization Tools](https://mlsanity.com/paper/2201.06433/) (2022)
- [A prediction and behavioural analysis of machine learning methods for modelling travel mode choice](https://mlsanity.com/paper/2301.04404/) (2023)
- [Deep Neural Networks for Choice Analysis: Architectural Design with Alternative-Specific Utility Functions](https://mlsanity.com/paper/1909.07481/) (2019)

## Built on by (most cited first, 3 of 3)

- [Functional effects models: Accounting for preference heterogeneity in panel data with machine learning](https://mlsanity.com/paper/2509.18047/) (2025)
- [ParamBoost: Gradient Boosted Piecewise Cubic Polynomials](https://mlsanity.com/paper/2604.18864/) (2026)
- [Better Capturing Interactions Between Products in~Retail: Revisited Negative Sampling for~Basket Choice Modeling](https://mlsanity.com/paper/2610.17963/) (2026)

## Abstract (arXiv)

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.