On the identifiability of causal graphs with multiple environments

ICLR 2026 Conference SubmissionAnonymous Authors
causal discovery; heterogeneous data; multiple environment; nonlinear independent component analysis
Abstract:

Causal discovery from i.i.d. observational data is known to be generally ill-posed. We demonstrate that if we have access to the distribution induced by a structural causal model, and additional data from (in the best case) only two environments that sufficiently differ in the noise statistics, the unique causal graph is identifiable. Notably, this is the first result in the literature that guarantees the entire causal graph recovery with a constant number of environments and arbitrary nonlinear mechanisms. Our only constraint is the Gaussianity of the noise terms; however, we propose potential ways to relax this requirement. Of interest on its own, we expand on the well-known duality between independent component analysis (ICA) and causal discovery; recent advancements have shown that nonlinear ICA can be solved from multiple environments, at least as many as the number of sources: we show that the same can be achieved for causal discovery while having access to much less auxiliary information.

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Overview

Overall Novelty Assessment

The paper establishes identifiability of causal graphs from only two environments with arbitrary nonlinear mechanisms, requiring Gaussian noise. It resides in the 'Identifiability Theory for Latent Causal Variables' leaf, which contains six papers total, indicating a moderately populated research direction within causal representation learning. This leaf focuses on theoretical guarantees for recovering latent causal structures from multi-environment data, distinguishing it from empirical or application-focused branches. The constant-environment requirement (two vs. scaling with graph size) positions this work as addressing a fundamental efficiency question in the subfield.

The taxonomy reveals neighboring leaves addressing multi-node interventions and temporal dynamics, both requiring different forms of environmental variation. The sibling papers in this leaf explore related identifiability conditions: some assume known intervention targets, others require more environments or impose parametric constraints. The broader 'Causal Representation Learning' branch contrasts with 'Causal Discovery from Observed Variables,' where methods like constraint-based approaches handle observed graphs without latent variable complications. The scope note clarifies this leaf excludes purely empirical methods, emphasizing the paper's theoretical orientation within a landscape balancing identifiability theory against practical algorithm design.

Among thirty candidates examined, the first contribution (two-environment identifiability with nonlinear mechanisms) shows no clear refutation across ten candidates, suggesting potential novelty in reducing environment requirements. The second contribution (ICA-causality duality proof techniques) similarly lacks refutable prior work among ten examined candidates, though the limited search scope means exhaustive coverage is uncertain. The third contribution (empirical validation on bivariate models) encountered one refutable candidate among ten, indicating some overlap in experimental methodology. These statistics reflect a focused semantic search, not comprehensive field coverage, leaving open whether broader literature contains closer precedents.

The analysis suggests the core theoretical contributions appear relatively novel within the examined scope, particularly the constant-environment guarantee. However, the limited search (thirty candidates from semantic matching) cannot rule out relevant work outside top-ranked results or in adjacent subfields like nonlinear ICA. The taxonomy structure shows this is an active area with multiple competing approaches to identifiability, so claims of 'first result' warrant careful verification against the full sibling paper set and recent preprints not captured here.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
30
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: causal graph identifiability from multiple environments. The field centers on leveraging heterogeneity across environments—whether through interventions, distributional shifts, or domain variations—to identify causal structures that remain unidentifiable from single-environment data. The taxonomy reveals several complementary branches: Causal Representation Learning from Multi-Environment Data focuses on recovering latent causal variables and their relationships from high-dimensional observations, often using identifiability theory to guarantee unique solutions under certain assumptions (e.g., CITRIS[1], Linearly Mixed Causal Representations[4]). Causal Discovery from Observed Variables Across Environments tackles structure learning when variables are directly observed, exploiting environment-specific changes to disambiguate causal directions (e.g., Causal Discovery Multiple Environments[3]). Invariance-Based Causal Inference and Prediction emphasizes finding stable predictive relationships that generalize across settings, while Domain-Specific Applications and Extensions adapt these principles to areas like genomics or reinforcement learning, and Meta-Learning and Algorithmic Frameworks develop scalable computational strategies. Recent work has intensified around identifiability guarantees for latent causal models, exploring how different types of environmental variation—interventions, nonstationarity, or context shifts—enable unique recovery of causal graphs. A central tension involves balancing generality of assumptions (e.g., nonparametric settings in Nonparametric Identifiability Unknown Interventions[5]) against practical tractability and sample efficiency. Causal Graphs Multiple Environments[0] sits squarely within the identifiability theory for latent causal variables, closely aligned with works like General Identifiability Achievability[37] and Linear Causal General Environments[16], which similarly investigate sufficient conditions for graph recovery under varied environment types. Compared to neighbors such as Latent Neural Causal[38], which emphasizes neural architectures for representation learning, the original paper[0] appears more focused on foundational identifiability conditions, establishing when and why multi-environment data provably resolves causal ambiguities that single-domain observations cannot.

Claimed Contributions

Identifiability of causal graphs from two environments with arbitrary nonlinear mechanisms

The authors prove that the entire causal graph of a structural causal model with arbitrary nonlinear mechanisms can be uniquely identified using data from only two sufficiently different environments, requiring only Gaussian noise terms. This is the first result guaranteeing full graph recovery with a constant number of environments.

10 retrieved papers
Novel proof techniques leveraging ICA-causality duality for multi-environment causal discovery

The authors develop new proof techniques that exploit the connection between independent component analysis and causal discovery, showing that causal graph identifiability requires fewer environments than ICA identifiability because it only needs to recover the Jacobian support at a single point rather than exact values everywhere.

10 retrieved papers
Empirical validation on bivariate models demonstrating causal direction inference

The authors provide experimental evidence on synthetic bivariate causal models showing that their method can correctly infer causal direction for previously non-identifiable cases when theoretical assumptions are satisfied, including linear Gaussian models and arbitrary nonlinear mechanisms.

10 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Identifiability of causal graphs from two environments with arbitrary nonlinear mechanisms

The authors prove that the entire causal graph of a structural causal model with arbitrary nonlinear mechanisms can be uniquely identified using data from only two sufficiently different environments, requiring only Gaussian noise terms. This is the first result guaranteeing full graph recovery with a constant number of environments.

Contribution

Novel proof techniques leveraging ICA-causality duality for multi-environment causal discovery

The authors develop new proof techniques that exploit the connection between independent component analysis and causal discovery, showing that causal graph identifiability requires fewer environments than ICA identifiability because it only needs to recover the Jacobian support at a single point rather than exact values everywhere.

Contribution

Empirical validation on bivariate models demonstrating causal direction inference

The authors provide experimental evidence on synthetic bivariate causal models showing that their method can correctly infer causal direction for previously non-identifiable cases when theoretical assumptions are satisfied, including linear Gaussian models and arbitrary nonlinear mechanisms.

On the identifiability of causal graphs with multiple environments | Novelty Validation