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Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 8.0Download Report PDF
causal discoverylatent variablesequivalencerank constraintslinear non-Gaussian modelscycles
Abstract:

Causal discovery with latent variables is a fundamental task. Yet most existing methods, if not all, rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We argue that a core obstacle to a general, structural-assumption-free approach is the lack of an equivalence characterization: without knowing what can be identified, one generally cannot design methods for how to identify it. In this work, we aim to close this gap for linear non-Gaussian models. We establish the graphical criterion for when two graphs with arbitrary latent structure and cycles are distributionally equivalent, that is, they induce the same observed distribution set. Key to our approach is a new tool, edge rank constraints, which fills a missing piece in the toolbox for latent-variable causal discovery in even broader settings. We further provide a procedure to traverse the whole equivalence class and develop an algorithm to recover models from data up to such equivalence. To our knowledge, this is the first equivalence characterization with latent variables in any parametric setting without structural assumptions, and hence the first structural-assumption-free discovery method. Code and an interactive demo are available at https://equiv.cc.

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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 establishes a graphical criterion for distributional equivalence in linear non-Gaussian models with arbitrary latent structure and cycles, introduces edge rank constraints as a new analytical tool, and proposes the glvLiNG algorithm for structural-assumption-free causal discovery. It resides in the 'General Identifiability Conditions' leaf alongside three sibling papers that also address identifiability without restricting latent variable interactions. This leaf sits within the broader 'Identifiability Theory and Equivalence Characterization' branch, which contains three leaves totaling nine papers, indicating a moderately populated but not overcrowded research direction focused on theoretical foundations.

The taxonomy reveals that neighboring leaves address 'Identifiability Under Restricted Latent Structure' (four papers assuming hierarchical or polytree arrangements) and 'Measurement Error and Proxy Variables' (two papers on noisy observations). The paper's structural-assumption-free approach contrasts with these restricted settings, positioning it closer to the general identifiability frontier. Adjacent branches include 'Algorithm Design and Methodology' (eighteen papers across six leaves) and 'Specialized Model Extensions' (five papers), suggesting that while algorithmic development is well-explored, foundational equivalence characterization in unrestricted settings remains less densely studied. The taxonomy's scope and exclude notes confirm that this work targets theoretical conditions rather than algorithm-centric contributions.

Among twenty-two candidates examined via limited semantic search, none clearly refute any of the three contributions. The graphical equivalence criterion examined five candidates with zero refutations, edge rank constraints examined seven with zero refutations, and the glvLiNG algorithm examined ten with zero refutations. This suggests that within the search scope, no prior work provides overlapping results for these specific contributions. However, the limited scale—twenty-two candidates rather than an exhaustive survey—means that relevant prior work outside the top semantic matches or citation network may exist. The absence of refutations across all contributions indicates either genuine novelty or gaps in the search coverage.

Based on the limited literature search, the work appears to occupy a relatively sparse area within general identifiability theory, with no immediate prior work overlapping its core contributions among the candidates examined. The taxonomy context shows that while the broader field is active, structural-assumption-free equivalence characterization remains underexplored compared to algorithm design or restricted-structure settings. The analysis covers top semantic matches and citation expansion but does not claim exhaustive coverage, leaving open the possibility of relevant work beyond the examined scope.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
22
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: Causal discovery with latent variables in linear non-Gaussian models. The field is organized around several complementary branches. Identifiability Theory and Equivalence Characterization establishes the theoretical foundations, clarifying when and under what conditions latent-variable structures can be uniquely recovered from observed data—works such as Parameter Identification Confounding[7] and Statistical Undecidability Latent[29] explore these boundaries. Algorithm Design and Methodology develops practical procedures, including constraint-based and score-based approaches like Score-based Latent Discovery[4] and Gradient-based Latent Discovery[50], while Specialized Model Extensions and Settings address nonlinear dynamics (Nonlinear Dynamic Latent[2]), measurement error (Measurement Error Discovery[14]), and hierarchical structures (Linear NonGaussian Hierarchical[3]). Additional branches cover Causal Effect Estimation and Inference, Model Validation and Testing (e.g., Goodness-of-fit LiNGAM[15]), Domain-Specific Applications, and Methodological Reviews. Special Latent Confounder Structures examine particular patterns such as instrumental variables and repetitive confounding. A central tension across these branches concerns the trade-off between identifiability guarantees and model flexibility: stronger non-Gaussian assumptions enable finer-grained recovery of latent structures, yet relaxing these assumptions often leads to partial identification or equivalence classes. Within Identifiability Theory, Distributional Equivalence Cyclic[0] investigates general conditions for distinguishing models under latent confounding, situating itself alongside Parameter Identification Confounding[7], which focuses on parameter-level uniqueness, and General Confounding Estimation[31], which addresses broader estimation frameworks. While Parameter Identification Confounding[7] emphasizes sufficient conditions for parameter recovery and General Confounding Estimation[31] targets practical inference strategies, Distributional Equivalence Cyclic[0] contributes by characterizing when different causal graphs yield indistinguishable distributions—a foundational question that informs both algorithmic design and the interpretation of empirical results. This line of work underscores ongoing challenges in balancing theoretical rigor with computational tractability when latent variables are present.

Claimed Contributions

Graphical criterion for distributional equivalence in linear non-Gaussian latent-variable cyclic models

The authors provide the first equivalence characterization for linear non-Gaussian models that allows arbitrary latent variables and cycles without structural assumptions. This characterization determines when two causal graphs induce the same observed distribution set.

5 retrieved papers
Edge rank constraints as a new tool for latent-variable causal discovery

The authors introduce edge rank constraints, a local edge-level constraint that complements path ranks. This tool enables easier manipulation of rank-based conditions and has potential applications across broader causal discovery settings beyond the specific linear non-Gaussian framework.

7 retrieved papers
glvLiNG algorithm for structural-assumption-free latent-variable causal discovery

The authors develop glvLiNG, a constraint-based algorithm that recovers causal models with latent variables from data up to distributional equivalence. This is claimed to be the first method that does not require structural assumptions about how latent variables interact with observed variables.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Graphical criterion for distributional equivalence in linear non-Gaussian latent-variable cyclic models

The authors provide the first equivalence characterization for linear non-Gaussian models that allows arbitrary latent variables and cycles without structural assumptions. This characterization determines when two causal graphs induce the same observed distribution set.

Contribution

Edge rank constraints as a new tool for latent-variable causal discovery

The authors introduce edge rank constraints, a local edge-level constraint that complements path ranks. This tool enables easier manipulation of rank-based conditions and has potential applications across broader causal discovery settings beyond the specific linear non-Gaussian framework.

Contribution

glvLiNG algorithm for structural-assumption-free latent-variable causal discovery

The authors develop glvLiNG, a constraint-based algorithm that recovers causal models with latent variables from data up to distributional equivalence. This is claimed to be the first method that does not require structural assumptions about how latent variables interact with observed variables.

Table of Contents

Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning | Novelty Validation