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Characterization and Learning of Causal Graphs with Latent Confounders and Post-treatment Selection from Interventional Data

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 7.5Download Report PDF
Post-treatment selectionSelection biasinterventional causal discovery
Abstract:

Interventional causal discovery seeks to identify causal relations by leveraging distributional changes introduced by interventions, even in the presence of latent confounders. Beyond the spurious dependencies induced by latent confounders, we highlight a common yet often overlooked challenge in the problem due to post-treatment selection, in which samples are selectively included in datasets after interventions. This fundamental challenge widely exists in biological studies; for example, in gene expression analysis, both observational and interventional samples are retained only if they meet quality control criteria (e.g., highly active cells). Neglecting post-treatment selection may introduce spurious dependencies and distributional changes under interventions, which can mimic causal responses, thereby distorting causal discovery results and challenging existing causal formulations. To address this, we introduce a novel causal formulation that explicitly models post-treatment selection and reveals how its differential reactions to interventions can distinguish causal relations from selection patterns, allowing us to go beyond traditional equivalence classes toward the underlying true causal structure. We then characterize its Markov properties and propose a F\mathcal{F}ine-grained I\mathcal{I}nterventional equivalence class, named FI\mathcal{FI}-Markov equivalence, represented by a new graphical diagram, F\mathcal{F}-PAG. Finally, we develop a provably sound and complete algorithm, F\mathcal{F}-FCI, to identify causal relations, latent confounders, and post-treatment selection up to FI\mathcal{FI}-Markov equivalence, using both observational and interventional data. Experimental results on synthetic and real-world datasets demonstrate that our method recovers causal relations despite the presence of both selection and latent confounders.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper introduces a causal formulation that explicitly models post-treatment selection alongside latent confounders in interventional causal discovery. It resides in the 'Discovery with Latent Confounders and Selection Bias' leaf, which contains four papers total (including this one). This leaf addresses a relatively specialized intersection of challenges—combining hidden confounding with selection mechanisms—suggesting a moderately sparse research direction within the broader interventional discovery landscape. The taxonomy shows that most discovery work either handles unknown intervention targets or focuses on time series, indicating that joint treatment of confounding and selection remains less crowded than other discovery subfields.

The taxonomy reveals neighboring leaves focused on unknown intervention targets, time series discovery, and cyclic structures, all under the 'Causal Discovery from Interventional Data' branch. The paper's leaf explicitly excludes methods handling only confounding or only selection, positioning it at a unique intersection. Nearby work on effect estimation (e.g., 'Effect Estimation with Hidden Confounding') addresses confounding but not structure learning, while 'Mediation Analysis with Post-Treatment Confounding' examines post-treatment variables in a different context. The taxonomy's scope notes clarify that this leaf is distinct from purely observational methods and from discovery approaches that assume known intervention targets, highlighting the paper's focus on a specific gap where selection bias meets interventional structure learning.

Among 28 candidates examined across three contributions, none were flagged as clearly refuting any contribution. Contribution A (novel causal formulation) examined 9 candidates with 0 refutable; Contribution B (FI-Markov equivalence and F-PAG) examined 9 with 0 refutable; Contribution C (F-FCI algorithm) examined 10 with 0 refutable. This suggests that within the limited search scope, no prior work was found that directly anticipates the joint modeling of post-treatment selection and latent confounders in interventional discovery. The absence of refutable candidates across all contributions indicates that the specific formulation and algorithmic framework appear novel relative to the examined literature, though the search was not exhaustive.

Based on the limited search of 28 candidates and the taxonomy structure, the work appears to occupy a relatively underexplored niche. The leaf contains only four papers, and no examined candidates refute the core contributions, suggesting that the explicit treatment of post-treatment selection in interventional discovery with latent confounders is not yet well-covered. However, this assessment is constrained by the search scope and does not rule out relevant work outside the top-K semantic matches or citation network examined.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
28
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: interventional causal discovery with latent confounders and post-treatment selection. This field addresses the challenge of learning causal structures from experimental or interventional data when some confounding variables remain unmeasured and when selection mechanisms operate after treatment assignment. The taxonomy organizes research into several main branches. Causal Discovery from Interventional Data focuses on algorithms that exploit experimental manipulations to identify causal graphs, including methods that handle unknown intervention targets (Unknown Intervention Targets[1]) or soft interventions (Soft Interventions Discovery[2]). Causal Effect Estimation and Inference develops techniques for quantifying treatment effects under various complications such as hidden confounding or selection bias. Machine Learning Integration with Causal Inference bridges modern predictive models with causal reasoning, while Methodological Foundations and Theoretical Advances establish identifiability conditions and statistical guarantees. Domain-Specific Applications translate these methods to healthcare, policy evaluation, and other real-world settings where latent confounders and selection are pervasive. A particularly active line of work examines the interplay between selection bias and interventional data, exploring when and how experimental information can overcome post-treatment selection issues that would otherwise obscure causal relationships. Within this landscape, Latent Confounders Interventional[0] sits at the intersection of discovery methods that must simultaneously address hidden confounding and selection mechanisms, closely related to Selection Meets Intervention[6] which explicitly studies how selection processes interact with experimental designs. Nearby works such as Iterative Causal Discovery[9] and Distinguishability Causal Structures[15] tackle complementary challenges: iterative refinement of causal hypotheses and the fundamental question of when different causal models can be distinguished from interventional distributions. These studies collectively highlight a central trade-off between the richness of interventional information available and the complexity of latent structure one can hope to recover, with ongoing questions about minimal experimental designs and the role of parametric or independence assumptions in achieving identifiability.

Claimed Contributions

Novel causal formulation modeling post-treatment selection with latent confounders

The authors propose a new causal framework that explicitly incorporates post-treatment selection alongside latent confounders. This formulation leverages differential responses to interventions to distinguish genuine causal relations from spurious dependencies induced by selection bias, addressing a gap in existing interventional causal discovery paradigms.

9 retrieved papers
FI-Markov equivalence and F-PAG graphical representation

The authors define a Fine-grained Interventional Markov equivalence class (FI-Markov equivalence) that refines traditional equivalence classes by exploiting interventional data. They introduce F-PAG, an extension of the Partial Ancestral Graph with novel edge types, to provide a more expressive graphical representation of this equivalence class.

9 retrieved papers
F-FCI algorithm for causal discovery with soundness and completeness guarantees

The authors develop the F-FCI algorithm, which recovers causal structures, latent confounders, and post-treatment selection up to FI-Markov equivalence from observational and interventional data. The algorithm is proven to be both sound and complete under the proposed formulation.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Novel causal formulation modeling post-treatment selection with latent confounders

The authors propose a new causal framework that explicitly incorporates post-treatment selection alongside latent confounders. This formulation leverages differential responses to interventions to distinguish genuine causal relations from spurious dependencies induced by selection bias, addressing a gap in existing interventional causal discovery paradigms.

Contribution

FI-Markov equivalence and F-PAG graphical representation

The authors define a Fine-grained Interventional Markov equivalence class (FI-Markov equivalence) that refines traditional equivalence classes by exploiting interventional data. They introduce F-PAG, an extension of the Partial Ancestral Graph with novel edge types, to provide a more expressive graphical representation of this equivalence class.

Contribution

F-FCI algorithm for causal discovery with soundness and completeness guarantees

The authors develop the F-FCI algorithm, which recovers causal structures, latent confounders, and post-treatment selection up to FI-Markov equivalence from observational and interventional data. The algorithm is proven to be both sound and complete under the proposed formulation.

Table of Contents

Characterization and Learning of Causal Graphs with Latent Confounders and Post-treatment Selection from Interventional Data | Novelty Validation