# A Nonparametric Approach with Marginals for Modeling Consumer Choice

arXiv: https://arxiv.org/abs/2208.06115 · HTML: https://mlsanity.com/paper/2208.06115/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 63 references that are in the map.
- First posted on arXiv 12 Aug 2022.

## Builds on (most cited first, 9 of 9)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution](https://mlsanity.com/paper/2103.06263/) (2021)
- [Representing Random Utility Choice Models with Neural Networks](https://mlsanity.com/paper/2207.12877/) (2022)
- [Decision Forest: A Nonparametric Approach to Modeling Irrational Choice](https://mlsanity.com/paper/1904.11532/) (2019)
- [Assortment optimisation under a general discrete choice model: A tight analysis of revenue-ordered assortments](https://mlsanity.com/paper/1606.01371/) (2016)
- [The Value of Robust Assortment Optimization Under Ranking-based Choice Models](https://mlsanity.com/paper/2112.05010/) (2021)
- [The Use of Binary Choice Forests to Model and Estimate Discrete Choices](https://mlsanity.com/paper/1908.01109/) (2019)
- [On the Global Convergence of Stochastic Fictitious Play in Stochastic Games with Turn-based Controllers](https://mlsanity.com/paper/2204.01382/) (2022)

## Built on by (most cited first, 2 of 2)

- [Going from a Representative Agent to Counterfactuals in Combinatorial Choice](https://mlsanity.com/paper/2505.23546/) (2025)
- [The Value of Human Expertise](https://mlsanity.com/paper/2608.26051/) (2026)

## Abstract (arXiv)

Given data on the choices made by consumers for different offer sets, a key challenge is to develop parsimonious models that describe and predict consumer choice behavior while being amenable to prescriptive tasks such as pricing and assortment optimization. The marginal distribution model (MDM) is one such model, which requires only the specification of marginal distributions of the random utilities. This paper aims to establish necessary and sufficient conditions for given choice data to be consistent with the MDM hypothesis, inspired by the usefulness of similar characterizations for the random utility model (RUM). This endeavor leads to an exact characterization of the set of choice probabilities that the MDM can represent. Verifying the consistency of choice data with this characterization is equivalent to solving a polynomial-sized linear program. Since the analogous verification task for RUM is computationally intractable and neither of these models subsumes the other, MDM is helpful in striking a balance between tractability and representational power. The characterization is then used with robust optimization for making data-driven sales and revenue predictions for new unseen assortments. When the choice data lacks consistency with the MDM hypothesis, finding the best-fitting MDM choice probabilities reduces to solving a mixed integer convex program. Numerical results using real world data and synthetic data demonstrate that MDM exhibits competitive representational power and prediction performance compared to RUM and parametric models while being significantly faster in computation than RUM.