# Kernel Conditional Moment Constraints for Confounding Robust Inference

arXiv: https://arxiv.org/abs/2302.13348 · HTML: https://mlsanity.com/paper/2302.13348/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 26 Feb 2023.

## Builds on (most cited first, 17 of 17)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [Distributionally Robust Optimization and Generalization in Kernel Methods](https://mlsanity.com/paper/1905.10943/) (2019)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Balanced Policy Evaluation and Learning](https://mlsanity.com/paper/1705.07384/) (2017)
- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [Fair Kernel Learning](https://mlsanity.com/paper/1710.05578/) (2017)
- [Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap](https://mlsanity.com/paper/1711.11286/) (2017)
- [Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing](https://mlsanity.com/paper/2102.04543/) (2021)
- [Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments](https://mlsanity.com/paper/2012.10315/) (2020)
- [Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding](https://mlsanity.com/paper/2112.11449/) (2021)
- [Kernel Conditional Moment Test via Maximum Moment Restriction](https://mlsanity.com/paper/2002.09225/) (2020)
- [Hard Shape-Constrained Kernel Machines](https://mlsanity.com/paper/2005.12636/) (2020)
- [Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictions](https://mlsanity.com/paper/2207.04771/) (2022)
- [Worst-Case Risk Quantification under Distributional Ambiguity using Kernel Mean Embedding in Moment Problem](https://mlsanity.com/paper/2004.00166/) (2020)

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

- [Predictive Performance Comparison of Decision Policies Under Confounding](https://mlsanity.com/paper/2404.00848/) (2024)
- [A Convex Framework for Confounding Robust Inference](https://mlsanity.com/paper/2309.12450/) (2023)

## Abstract (arXiv)

We study policy evaluation of offline contextual bandits subject to unobserved confounders. Sensitivity analysis methods are commonly used to estimate the policy value under the worst-case confounding over a given uncertainty set. However, existing work often resorts to some coarse relaxation of the uncertainty set for the sake of tractability, leading to overly conservative estimation of the policy value. In this paper, we propose a general estimator that provides a sharp lower bound of the policy value. It can be shown that our estimator contains the recently proposed sharp estimator by Dorn and Guo (2022) as a special case, and our method enables a novel extension of the classical marginal sensitivity model using f-divergence. To construct our estimator, we leverage the kernel method to obtain a tractable approximation to the conditional moment constraints, which traditional non-sharp estimators failed to take into account. In the theoretical analysis, we provide a condition for the choice of the kernel which guarantees no specification error that biases the lower bound estimation. Furthermore, we provide consistency guarantees of policy evaluation and learning. In the experiments with synthetic and real-world data, we demonstrate the effectiveness of the proposed method.