# Choice Models and Permutation Invariance: Demand Estimation in Differentiated Products Markets

arXiv: https://arxiv.org/abs/2307.07090 · HTML: https://mlsanity.com/paper/2307.07090/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 96 references that are in the map.
- First posted on arXiv 13 Jul 2023.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [On the Limitations of Representing Functions on Sets](https://mlsanity.com/paper/1901.09006/) (2019)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression](https://mlsanity.com/paper/1508.03365/) (2015)
- [A Neural-embedded Choice Model: TasteNet-MNL Modeling Taste Heterogeneity with Flexibility and Interpretability](https://mlsanity.com/paper/2002.00922/) (2020)
- [Representing Random Utility Choice Models with Neural Networks](https://mlsanity.com/paper/2207.12877/) (2022)
- [Causal Gradient Boosting: Boosted Instrumental Variable Regression](https://mlsanity.com/paper/2101.06078/) (2021)
- [Deep Learning for Choice Modeling](https://mlsanity.com/paper/2208.09325/) (2022)
- [Estimating Semi-parametric Panel Multinomial Choice Models using Cyclic Monotonicity](https://mlsanity.com/paper/1604.06145/) (2016)

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

- [Amortized Inference for Correlated Discrete Choice Models via Equivariant Neural Networks](https://mlsanity.com/paper/2603.24705/) (2026)
- [Penalized GMM Framework for Inference on Functionals of Nonparametric Instrumental Variable Estimators](https://mlsanity.com/paper/2603.29889/) (2026)

## Abstract (arXiv)

Choice modeling is at the core of understanding how changes to the competitive landscape affect consumer choices and reshape market equilibria. In this paper, we propose a fundamental characterization of choice functions that encompasses a wide variety of extant choice models. We demonstrate how non-parametric estimators like neural nets can easily approximate such functionals and overcome the curse of dimensionality that is inherent in the non-parametric estimation of choice functions. We demonstrate through extensive simulations that our proposed functionals can flexibly capture underlying consumer behavior in a completely data-driven fashion and outperform traditional parametric models. As demand settings often exhibit endogenous features, we extend our framework to incorporate estimation under endogenous features. Further, we also describe a formal inference procedure to construct valid confidence intervals on objects of interest like price elasticity. Finally, to assess the practical applicability of our estimator, we utilize a real-world dataset from S. Berry, Levinsohn, and Pakes (1995). Our empirical analysis confirms that the estimator generates realistic and comparable own- and cross-price elasticities that are consistent with the observations reported in the existing literature.