# Counterfactual Density Estimation using Kernel Stein Discrepancies

arXiv: https://arxiv.org/abs/2309.16129 · HTML: https://mlsanity.com/paper/2309.16129/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2023.

## Built on by (most cited first, 7 of 7)

- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [Scalable Counterfactual Distribution Estimation in Multivariate Causal Models](https://mlsanity.com/paper/2311.00927/) (2023)
- [Nystr"om Kernel Stein Discrepancy](https://mlsanity.com/paper/2406.08401/) (2024)
- [GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomes](https://mlsanity.com/paper/2509.22953/) (2025)
- [Debiased Counterfactual Generation via Flow Matching from Observations](https://mlsanity.com/paper/2605.07665/) (2026)
- [Limits of Approximating the Median Treatment Effect](https://mlsanity.com/paper/2403.10618/) (2024)
- [Testing for Causal Fairness](https://mlsanity.com/paper/2502.12874/) (2025)

## Abstract (arXiv)

Causal effects are usually studied in terms of the means of counterfactual distributions, which may be insufficient in many scenarios. Given a class of densities known up to normalizing constants, we propose to model counterfactual distributions by minimizing kernel Stein discrepancies in a doubly robust manner. This enables the estimation of counterfactuals over large classes of distributions while exploiting the desired double robustness. We present a theoretical analysis of the proposed estimator, providing sufficient conditions for consistency and asymptotic normality, as well as an examination of its empirical performance.