# Robust and Heterogenous Odds Ratio: Estimating Price Sensitivity for Unbought Items

arXiv: https://arxiv.org/abs/2106.11389 · HTML: https://mlsanity.com/paper/2106.11389/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 86 references that are in the map.
- First posted on arXiv 21 Jun 2021.

## Builds on (most cited first, 16 of 16)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [European Union regulations on algorithmic decision-making and a "right to explanation"](https://mlsanity.com/paper/1606.08813/) (2016)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Generalized and Scalable Optimal Sparse Decision Trees](https://mlsanity.com/paper/2006.08690/) (2020)
- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [Offline Multi-Action Policy Learning: Generalization and Optimization](https://mlsanity.com/paper/1810.04778/) (2018)
- [MurTree: Optimal Classification Trees via Dynamic Programming and Search](https://mlsanity.com/paper/2007.12652/) (2020)
- [Orthogonal Random Forest for Causal Inference](https://mlsanity.com/paper/1806.03467/) (2018)
- [Recursive Partitioning for Personalization using Observational Data](https://mlsanity.com/paper/1608.08925/) (2016)
- [Interpretable Optimal Stopping](https://mlsanity.com/paper/1812.07211/) (2018)
- [Robust Recursive Partitioning for Heterogeneous Treatment Effects with Uncertainty Quantification](https://mlsanity.com/paper/2006.07917/) (2020)
- [Decision Forest: A Nonparametric Approach to Modeling Irrational Choice](https://mlsanity.com/paper/1904.11532/) (2019)
- [Learning Triggers for Heterogeneous Treatment Effects](https://mlsanity.com/paper/1902.00087/) (2019)
- [Heterogeneous causal effects with imperfect compliance: a Bayesian machine learning approach](https://mlsanity.com/paper/1905.12707/) (2019)
- [SIRUS: Stable and Interpretable RUle Set for Classification](https://mlsanity.com/paper/1908.06852/) (2019)

## Abstract (arXiv)

Problem definition: Mining for heterogeneous responses to an intervention is a crucial step for data-driven operations, for instance to personalize treatment or pricing. We investigate how to estimate price sensitivity from transaction-level data. In causal inference terms, we estimate heterogeneous treatment effects when (a) the response to treatment (here, whether a customer buys a product) is binary, and (b) treatment assignments are partially observed (here, full information is only available for purchased items). Methodology/Results: We propose a recursive partitioning procedure to estimate heterogeneous odds ratio, a widely used measure of treatment effect in medicine and social sciences. We integrate an adversarial imputation step to allow for robust estimation even in presence of partially observed treatment assignments. We validate our methodology on synthetic data and apply it to three case studies from political science, medicine, and revenue management. Managerial Implications: Our robust heterogeneous odds ratio estimation method is a simple and intuitive tool to quantify heterogeneity in patients or customers and personalize interventions, while lifting a central limitation in many revenue management data.