# Finding Valid Adjustments under Non-ignorability with Minimal DAG Knowledge

arXiv: https://arxiv.org/abs/2106.11560 · HTML: https://mlsanity.com/paper/2106.11560/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 65 references that are in the map.
- First posted on arXiv 22 Jun 2021.

## Builds on (most cited first, 22 of 22)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [Does Invariant Risk Minimization Capture Invariance?](https://mlsanity.com/paper/2101.01134/) (2021)
- [Off-policy evaluation for slate recommendation](https://mlsanity.com/paper/1605.04812/) (2016)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Training](https://mlsanity.com/paper/1802.05664/) (2018)
- [Learning and Testing Causal Models with Interventions](https://mlsanity.com/paper/1805.09697/) (2018)
- [Out-of-distribution Prediction with Invariant Risk Minimization: The Limitation and An Effective Fix](https://mlsanity.com/paper/2101.07732/) (2021)
- [Invariant Representation Learning for Treatment Effect Estimation](https://mlsanity.com/paper/2011.12379/) (2020)
- [An Evaluation Toolkit to Guide Model Selection and Cohort Definition in Causal Inference](https://mlsanity.com/paper/1906.00442/) (2019)
- [Differentiable Causal Backdoor Discovery](https://mlsanity.com/paper/2003.01461/) (2020)
- [Treatment Effect Estimation using Invariant Risk Minimization](https://mlsanity.com/paper/2103.07788/) (2021)

## Built on by (most cited first, 10 of 10)

- [Local Causal Discovery for Estimating Causal Effects](https://mlsanity.com/paper/2302.08070/) (2023)
- [Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around Exposure-Outcome Pairs](https://mlsanity.com/paper/2310.17816/) (2023)
- [On Testability of the Front-Door Model via Verma Constraints](https://mlsanity.com/paper/2203.00161/) (2022)
- [Finding and Listing Front-door Adjustment Sets](https://mlsanity.com/paper/2210.05816/) (2022)
- [Local Causal Discovery for Structural Evidence of Direct Discrimination](https://mlsanity.com/paper/2405.14848/) (2024)
- [Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Models](https://mlsanity.com/paper/2405.14496/) (2024)
- [Front-door Adjustment Beyond Markov Equivalence with Limited Graph Knowledge](https://mlsanity.com/paper/2306.11008/) (2023)
- [Probably approximately correct high-dimensional causal effect estimation given a valid adjustment set](https://mlsanity.com/paper/2411.08141/) (2024)
- [PAC Generalization via Invariant Representations](https://mlsanity.com/paper/2205.15196/) (2022)
- [Representation Learning Preserving Ignorability and Covariate Matching for Treatment Effects](https://mlsanity.com/paper/2504.20579/) (2025)

## Abstract (arXiv)

Treatment effect estimation from observational data is a fundamental problem in causal inference. There are two very different schools of thought that have tackled this problem. On one hand, Pearlian framework commonly assumes structural knowledge (provided by an expert) in form of directed acyclic graphs and provides graphical criteria such as back-door criterion to identify valid adjustment sets. On other hand, potential outcomes (PO) framework commonly assumes that all observed features satisfy ignorability (i.e., no hidden confounding), which in general is untestable. In prior works that attempted to bridge these frameworks, there is an observational criteria to identify an anchor variable and if a subset of covariates (not involving the anchor variable) passes a suitable conditional independence criteria, then that subset is a valid back-door. Our main result strengthens these prior results by showing that under a different expert-driven structural knowledge -- that one variable is a direct causal parent of treatment variable -- remarkably, testing for subsets (not involving the known parent variable) that are valid back-doors is equivalent to an invariance test. Importantly, we also cover the non-trivial case where entire set of observed features is not ignorable (generalizing the PO framework) without requiring knowledge of all parents of treatment variable. Our key technical idea involves generation of a synthetic sub-sampling (or environment) variable that is a function of the known parent variable. In addition to designing an invariance test, this sub-sampling variable allows us to leverage Invariant Risk Minimization, and thus, connects finding valid adjustments (in non-ignorable observational setting) to representation learning. We demonstrate effectiveness and tradeoffs of our approaches on a variety of synthetic data as well as real causal effect estimation benchmarks.