Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variables
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Abstract (arXiv)
The problem of selecting optimal backdoor adjustment sets to estimate causal effects in graphical models with hidden and conditioned variables is addressed. Previous work has defined optimality as achieving the smallest asymptotic estimation variance and derived an optimal set for the case without hidden variables. For the case with hidden variables there can be settings where no optimal set exists and currently only a sufficient graphical optimality criterion of limited applicability has been derived. In the present work optimality is characterized as maximizing a certain adjustment information which allows to derive a necessary and sufficient graphical criterion for the existence of an optimal adjustment set and a definition and algorithm to construct it. Further, the optimal set is valid if and only if a valid adjustment set exists and has higher (or equal) adjustment information than the Adjust-set proposed in Perkovi'c et al. [Journal of Machine Learning Research, 18: 1--62, 2018] for any graph. The results translate to minimal asymptotic estimation variance for a class of estimators whose asymptotic variance follows a certain information-theoretic relation. Numerical experiments indicate that the asymptotic results also hold for relatively small sample sizes and that the optimal adjustment set or minimized variants thereof often yield better variance also beyond that estimator class. Surprisingly, among the randomly created setups more than 90% fulfill the optimality conditions indicating that also in many real-world scenarios graphical optimality may hold. Code is available as part of the python package urlhttps://github.com/jakobrunge/tigramite.
Key facts. Cited by 16 papers in the map (data through 13 Oct 2026). Builds on 4 of its 26 references that are in the map. First posted on arXiv 20 Feb 2021.
Builds on
4 of 26 references.
References · 4
- 2018Separators and Adjustment Sets in Causal Graphs: Complete Criteria and an Algorithmic Frameworkcited by 16
- 2020Efficient adjustment sets in causal graphical models with hidden variablescited by 13
- 2013Markovian acyclic directed mixed graphs for discrete datacited by 10
- 2019Efficient adjustment sets for population average treatment effect estimation in non-parametric causal graphical modelscited by 7
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Citing papers per year: 2022: 2; 2023: 5; 2024: 6; 2025: 1; 2026: 2.
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- 2023Discovering Causal Relations and Equations from Datacited by 35
- 2023CUTS: Neural Causal Discovery from Irregular Time-Series Datacited by 33
- 2022Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Surveycited by 19
- 2023Identifiability of total effects from abstractions of time series causal graphscited by 13
- 2024Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshotscited by 12
- 2023Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around Exposure-Outcome Pairscited by 9
- 2024Separation-based distance measures for causal graphscited by 9
- 2024Local Causal Discovery for Structural Evidence of Direct Discriminationcited by 6
- 2024An Overview of Causal Inference using Kernel Embeddingscited by 5
- 2026Structural Causal Bottleneck Modelscited by 4
- 2024Local Learning for Covariate Selection in Nonparametric Causal Effect Estimation with Latent Variablescited by 3
- 2022A note on efficient minimum cost adjustment sets in causal graphical modelscited by 2
4 more
- 2026Unveiling the Structure of Do-Calculus Reasoning via Derivation Graphscited by 2
- 2023Projecting infinite time series graphs to finite marginal graphs using number theorycited by 0
- 2024Spatio-Temporal Graphical Counterfactuals: An Overviewcited by 0
- 2025On Efficient Adjustment for Micro Causal Effects in Summary Causal Graphscited by 0
- 2026Unveiling the Structure of Do-Calculus Reasoning via Derivation Graphs2 Jun 2026
- 2026Structural Causal Bottleneck Models9 Mar 2026
- 2025On Efficient Adjustment for Micro Causal Effects in Summary Causal Graphs20 Dec 2025
- 2024Local Learning for Covariate Selection in Nonparametric Causal Effect Estimation with Latent Variables25 Nov 2024
- 2024An Overview of Causal Inference using Kernel Embeddings30 Oct 2024
- 2024Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots30 Oct 2024
- 2024Spatio-Temporal Graphical Counterfactuals: An Overview2 Jul 2024
- 2024Local Causal Discovery for Structural Evidence of Direct Discrimination23 May 2024
- 2024Separation-based distance measures for causal graphs7 Feb 2024
- 2023Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around Exposure-Outcome Pairs25 Oct 2023
- 2023Identifiability of total effects from abstractions of time series causal graphs23 Oct 2023
- 2023Projecting infinite time series graphs to finite marginal graphs using number theory9 Oct 2023
4 more
- 2023Discovering Causal Relations and Equations from Data21 May 2023
- 2023CUTS: Neural Causal Discovery from Irregular Time-Series Data15 Feb 2023
- 2022Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Survey20 Aug 2022
- 2022A note on efficient minimum cost adjustment sets in causal graphical models6 Jan 2022
- 2023Discovering Causal Relations and Equations from Datacited by 35
- 2023CUTS: Neural Causal Discovery from Irregular Time-Series Datacited by 33
- 2022Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Surveycited by 19
- 2023Identifiability of total effects from abstractions of time series causal graphscited by 13
- 2024Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshotscited by 12
- 2023Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around Exposure-Outcome Pairscited by 9
- 2024Separation-based distance measures for causal graphscited by 9
- 2024Local Causal Discovery for Structural Evidence of Direct Discriminationcited by 6
- 2024An Overview of Causal Inference using Kernel Embeddingscited by 5
- 2026Structural Causal Bottleneck Modelscited by 4
- 2024Local Learning for Covariate Selection in Nonparametric Causal Effect Estimation with Latent Variablescited by 3
- 2022A note on efficient minimum cost adjustment sets in causal graphical modelscited by 2
12 most cited of 16 All 16 (JSON)
- 2026Unveiling the Structure of Do-Calculus Reasoning via Derivation Graphs2 Jun 2026
- 2026Structural Causal Bottleneck Models9 Mar 2026
- 2025On Efficient Adjustment for Micro Causal Effects in Summary Causal Graphs20 Dec 2025
- 2024Local Learning for Covariate Selection in Nonparametric Causal Effect Estimation with Latent Variables25 Nov 2024
- 2024An Overview of Causal Inference using Kernel Embeddings30 Oct 2024
- 2024Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots30 Oct 2024
- 2024Spatio-Temporal Graphical Counterfactuals: An Overview2 Jul 2024
- 2024Local Causal Discovery for Structural Evidence of Direct Discrimination23 May 2024
- 2024Separation-based distance measures for causal graphs7 Feb 2024
- 2023Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around Exposure-Outcome Pairs25 Oct 2023
- 2023Identifiability of total effects from abstractions of time series causal graphs23 Oct 2023
- 2023Projecting infinite time series graphs to finite marginal graphs using number theory9 Oct 2023
12 newest of 16 All 16 (JSON)
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