# Probably approximately correct high-dimensional causal effect estimation given a valid adjustment set

arXiv: https://arxiv.org/abs/2411.08141 · HTML: https://mlsanity.com/paper/2411.08141/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 101 references that are in the map.
- First posted on arXiv 12 Nov 2024.

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

- [A polynomial-time algorithm for learning nonparametric causal graphs](https://mlsanity.com/paper/2006.11970/) (2020)
- [Verification and search algorithms for causal DAGs](https://mlsanity.com/paper/2206.15374/) (2022)
- [Optimal estimation of Gaussian DAG models](https://mlsanity.com/paper/2201.10548/) (2022)
- [Subset verification and search algorithms for causal DAGs](https://mlsanity.com/paper/2301.03180/) (2023)
- [Debiased Inverse Propensity Score Weighting for Estimation of Average Treatment Effects with High-Dimensional Confounders](https://mlsanity.com/paper/2011.08661/) (2020)
- [Finding Valid Adjustments under Non-ignorability with Minimal DAG Knowledge](https://mlsanity.com/paper/2106.11560/) (2021)
- [Active causal structure learning with advice](https://mlsanity.com/paper/2305.19588/) (2023)
- [On the Sample Complexity of Causal Discovery and the Value of Domain Expertise](https://mlsanity.com/paper/2102.03274/) (2021)
- [Sparsity Double Robust Inference of Average Treatment Effects](https://mlsanity.com/paper/1905.00744/) (2019)
- [Adaptivity Complexity for Causal Graph Discovery](https://mlsanity.com/paper/2306.05781/) (2023)
- [Post-selection inference for causal effects after causal discovery](https://mlsanity.com/paper/2405.06763/) (2024)
- [High-Dimensional Feature Selection for Sample Efficient Treatment Effect Estimation](https://mlsanity.com/paper/2011.01979/) (2020)
- [A cautious approach to constraint-based causal model selection](https://mlsanity.com/paper/2404.18232/) (2024)
- [Causal Inference with High-dimensional Discrete Covariates](https://mlsanity.com/paper/2405.00118/) (2024)
- [New metrics and search algorithms for weighted causal DAGs](https://mlsanity.com/paper/2305.04445/) (2023)
- [Causal Razors](https://mlsanity.com/paper/2302.10331/) (2023)

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

- [CausalPFN: Amortized Causal Effect Estimation via In-Context Learning](https://mlsanity.com/paper/2506.07918/) (2025)
- [PAC-Causal Learnability: From Identification to Finite-Sample Guarantees](https://mlsanity.com/paper/2507.18903/) (2025)

## Abstract (arXiv)

Accurate estimates of causal effects play a key role in decision-making across applications such as healthcare, economics, and operations. In the absence of randomized experiments, a common approach to estimating causal effects uses textitcovariate adjustment. In this paper, we study covariate adjustment for discrete distributions from the PAC learning perspective, assuming knowledge of a valid adjustment set bZ, which might be high-dimensional. Our first main result PAC-bounds the estimation error of covariate adjustment by a term that is exponential in the size of the adjustment set; it is known that such a dependency is unavoidable even if one only aims to minimize the mean squared error. Motivated by this result, we introduce the notion of an eps-Markov blanket, give bounds on the misspecification error of using such a set for covariate adjustment, and provide an algorithm for eps-Markov blanket discovery; our second main result upper bounds the sample complexity of this algorithm. Furthermore, we provide a misspecification error bound and a constraint-based algorithm that allow us to go beyond eps-Markov blankets to even smaller adjustment sets. Our third main result upper bounds the sample complexity of this algorithm, and our final result combines the first three into an overall PAC bound. Altogether, our results highlight that one does not need to perfectly recover causal structure in order to ensure accurate estimates of causal effects.