# Data-Driven Influence Functions for Optimization-Based Causal Inference

arXiv: https://arxiv.org/abs/2208.13701 · HTML: https://mlsanity.com/paper/2208.13701/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 80 references that are in the map.
- First posted on arXiv 29 Aug 2022.

## Builds on (most cited first, 30 of 30)

- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Doubly Robust Off-policy Value Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1511.03722/) (2015)
- [Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1604.00923/) (2016)
- [Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation](https://mlsanity.com/paper/1810.12429/) (2018)
- [Optimal rates for zero-order convex optimization: the power of two function evaluations](https://mlsanity.com/paper/1312.2139/) (2013)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes](https://mlsanity.com/paper/1908.08526/) (2019)
- [Efficiently Breaking the Curse of Horizon in Off-Policy Evaluation with Double Reinforcement Learning](https://mlsanity.com/paper/1909.05850/) (2019)
- [Confounding-Robust Policy Evaluation in Infinite-Horizon Reinforcement Learning](https://mlsanity.com/paper/2002.04518/) (2020)
- [A Swiss Army Infinitesimal Jackknife](https://mlsanity.com/paper/1806.00550/) (2018)
- [RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forests](https://mlsanity.com/paper/2110.03031/) (2021)
- [Asymptotic Optimality in Stochastic Optimization](https://mlsanity.com/paper/1612.05612/) (2016)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [Adversarial Estimation of Riesz Representers](https://mlsanity.com/paper/2101.00009/) (2020)
- [Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding](https://mlsanity.com/paper/2112.11449/) (2021)
- [Localized Debiased Machine Learning: Efficient Inference on Quantile Treatment Effects and Beyond](https://mlsanity.com/paper/1912.12945/) (2019)
- [Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variables](https://mlsanity.com/paper/2003.12659/) (2020)
- [Randomized Automatic Differentiation](https://mlsanity.com/paper/2007.10412/) (2020)
- [Visually Communicating and Teaching Intuition for Influence Functions](https://mlsanity.com/paper/1810.03260/) (2018)
- [More Efficient Off-Policy Evaluation through Regularized Targeted Learning](https://mlsanity.com/paper/1912.06292/) (2019)
- [A Higher-Order Swiss Army Infinitesimal Jackknife](https://mlsanity.com/paper/1907.12116/) (2019)
- [Sensitivity analysis via the proportion of unmeasured confounding](https://mlsanity.com/paper/1912.02793/) (2019)
- [Debiasing In-Sample Policy Performance for Small-Data, Large-Scale Optimization](https://mlsanity.com/paper/2107.12438/) (2021)
- [Semiparametric sensitivity analysis: unmeasured confounding in observational studies](https://mlsanity.com/paper/2104.08300/) (2021)
- [Stochastic Primal-Dual Q-Learning](https://mlsanity.com/paper/1810.08298/) (2018)
- [Stateful Offline Contextual Policy Evaluation and Learning](https://mlsanity.com/paper/2110.10081/) (2021)
- [Assessing External Validity Over Worst-case Subpopulations](https://mlsanity.com/paper/2007.02411/) (2020)
- [Variance-based sensitivity analysis for weighting estimators result in more informative bounds](https://mlsanity.com/paper/2208.01691/) (2022)
- [Large-Scale Markov Decision Problems via the Linear Programming Dual](https://mlsanity.com/paper/1901.01992/) (2019)
- [Off-Policy Evaluation with Policy-Dependent Optimization Response](https://mlsanity.com/paper/2202.12958/) (2022)

## Built on by (most cited first, 1 of 1)

- [Automated Efficient Estimation using Monte Carlo Efficient Influence Functions](https://mlsanity.com/paper/2403.00158/) (2024)

## Abstract (arXiv)

We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing, with a focus on functionals that arise in causal inference. We study the case where probability distributions are not known a priori but need to be estimated from data. These estimated distributions lead to empirical Gateaux derivatives, and we study the relationships between empirical, numerical, and analytical Gateaux derivatives. Starting with a case study of the interventional mean (average potential outcome), we delineate the relationship between finite differences and the analytical Gateaux derivative. We then derive requirements on the rates of numerical approximation in perturbation and smoothing that preserve the statistical benefits of one-step adjustments, such as rate double robustness. We then study more complicated functionals such as dynamic treatment regimes, the linear-programming formulation for policy optimization in infinite-horizon Markov decision processes, and sensitivity analysis in causal inference. More broadly, we study optimization-based estimators, since this begets a class of estimands where identification via regression adjustment is straightforward but obtaining influence functions under minor variations thereof is not. The ability to approximate bias adjustments in the presence of arbitrary constraints illustrates the usefulness of constructive approaches for Gateaux derivatives. We also find that the statistical structure of the functional (rate double robustness) can permit less conservative rates for finite-difference approximation. This property, however, can be specific to particular functionals; e.g., it occurs for the average potential outcome (hence average treatment effect) but not the infinite-horizon MDP policy value.