mlsanityData to 7 Oct 2026

Finding Valid Adjustments under Non-ignorability with Minimal DAG Knowledge

arXiv 2106.11560 ↗First posted 22 Jun 2021cs.LGcited by 10

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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.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 22 of its 65 references that are in the map. First posted on arXiv 22 Jun 2021.

Builds on

22 of 65 references.

References · 22

  1. 2019Invariant Risk Minimizationcited by 1,832
  2. 2020Out-of-Distribution Generalization via Risk Extrapolation (REx)cited by 737
  3. 2015Estimation and Inference of Heterogeneous Treatment Effects using Random Forestscited by 597
  4. 2015Causal inference using invariant prediction: identification and confidence intervalscited by 533
  5. 2017Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learningcited by 475
  6. 2016Learning Representations for Counterfactual Inferencecited by 327
  7. 2019Adapting Neural Networks for the Estimation of Treatment Effectscited by 285
  8. 2019Causality for Machine Learningcited by 242
  9. 2017Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processescited by 156
  10. 2017Invariant Causal Prediction for Nonlinear Modelscited by 140
  11. 2017Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributionscited by 125
  12. 2021Does Invariant Risk Minimization Capture Invariance?cited by 116
10 more
  1. 2016Off-policy evaluation for slate recommendationcited by 102
  2. 2017Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discoverycited by 76
  3. 2013Causal Networks: Semantics and Expressivenesscited by 67
  4. 2018DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Trainingcited by 42
  5. 2018Learning and Testing Causal Models with Interventionscited by 29
  6. 2021Out-of-distribution Prediction with Invariant Risk Minimization: The Limitation and An Effective Fixcited by 27
  7. 2020Invariant Representation Learning for Treatment Effect Estimationcited by 25
  8. 2019An Evaluation Toolkit to Guide Model Selection and Cohort Definition in Causal Inferencecited by 18
  9. 2020Differentiable Causal Backdoor Discoverycited by 5
  10. 2021Treatment Effect Estimation using Invariant Risk Minimizationcited by 2

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Cited by year

Citing papers per year: 2022: 3; 2023: 3; 2024: 3; 2025: 1.

10 papers.

  1. 2023Local Causal Discovery for Estimating Causal Effectscited by 10
  2. 2023Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around Exposure-Outcome Pairscited by 9
  3. 2022On Testability of the Front-Door Model via Verma Constraintscited by 8
  4. 2022Finding and Listing Front-door Adjustment Setscited by 6
  5. 2024Local Causal Discovery for Structural Evidence of Direct Discriminationcited by 6
  6. 2024Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Modelscited by 5
  7. 2023Front-door Adjustment Beyond Markov Equivalence with Limited Graph Knowledgecited by 4
  8. 2024Probably approximately correct high-dimensional causal effect estimation given a valid adjustment setcited by 2
  9. 2022PAC Generalization via Invariant Representationscited by 1
  10. 2025Representation Learning Preserving Ignorability and Covariate Matching for Treatment Effectscited by 0