Causal Discovery in the Wild: A Voting-Theoretic Ensemble Approach

ICLR 2026 Conference SubmissionAnonymous Authors
Causal DiscoveryEnsemble Learning
Abstract:

Causal discovery is a critical yet persistently challenging task across scientific domains. Despite years of significant algorithmic advances, existing methods still struggle with inconsistent outcomes due to reliance on untestable assumptions, sensitivity to data perturbations, and optimization constraints. To this end, ensemble-based causal discovery has been actively pursued, aiming to aggregate multiple structural predictions for increased stability and uncertainty estimation. However, current aggregation methods are largely heuristic, lacking theoretical guarantees and guidance on how ensemble design choices affect performance. This work is proposed to address there fundamental limitations. We introduce a principled voting-based framework for structural ensembling, establishing conditions under which the aggregated structure recovers the true causal graph. Our analysis yields a theoretically justified weighted voting mechanism that informs optimal choices regarding the number, competency, and diversity of causal discovery experts in the ensemble. Extensive experiments on synthetic and real-world datasets verify the robustness and effectiveness of our approach, offering a rigorous alternative to existing heuristic ensemble methods.

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Overview

Overall Novelty Assessment

The paper proposes a principled voting-based framework for aggregating outputs from heterogeneous causal discovery algorithms, establishing theoretical conditions under which the ensemble recovers the true causal graph. It resides in the 'Voting-Based and Weighted Ensemble Aggregation' leaf, which contains only three papers including this work. This represents a relatively sparse research direction within the broader taxonomy of fifty papers, suggesting that theoretically grounded voting mechanisms for causal structure ensembling remain underexplored despite active interest in ensemble-based causal discovery more generally.

The taxonomy reveals that neighboring leaves address related but distinct challenges: 'Bootstrap and Confidence-Based Ensemble Methods' emphasizes stability through resampling rather than voting, while 'Algorithm Selection and Meta-Learning' focuses on choosing among algorithms rather than aggregating all outputs. The parent branch 'Ensemble Aggregation Frameworks and Theoretical Foundations' excludes domain-specific applications and distributed computation methods, positioning this work as a core methodological contribution to aggregation theory. Sibling papers in the same leaf explore weighted connectivity measures and algorithm selection evaluation, indicating that the field is actively seeking principled ways to combine heterogeneous discovery methods.

Among eight candidates examined across three contributions, none were identified as clearly refuting the proposed work. The first contribution (principled voting framework with theoretical guarantees) examined seven candidates with zero refutable matches, suggesting limited prior work establishing formal conditions for ensemble recovery of causal graphs. The second contribution (weighted voting mechanism informed by design factors) examined one candidate without refutation, while the third contribution (optimal transport for parameter estimation) examined no candidates. This limited search scope—eight total candidates rather than hundreds—means the analysis captures only a narrow slice of potentially relevant literature, primarily from top semantic matches.

The analysis suggests the work occupies a relatively novel position within a sparse research direction, though the small search scope (eight candidates) limits confidence in this assessment. The absence of refutable prior work among examined candidates may reflect either genuine novelty or incomplete coverage of the literature. The theoretical focus on voting mechanisms with formal guarantees appears less explored than heuristic aggregation approaches, but a more exhaustive search would be needed to confirm this impression definitively.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
8
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: ensemble-based causal discovery from heterogeneous algorithms. The field addresses how to combine outputs from diverse causal discovery methods to produce more robust and reliable causal graphs. The taxonomy reveals several major branches: Ensemble Aggregation Frameworks and Theoretical Foundations focuses on voting schemes, weighted combinations, and principled ways to merge heterogeneous algorithm outputs (e.g., Voting Ensemble[0], Weighted Ensemble Connectivity[11]); Scalable and Distributed Causal Discovery tackles computational challenges through federated learning and parallel approaches (e.g., Federated Local Learning[3], FedCSL[21]); Causal Discovery for Specialized Data Structures handles time series, spatial data, and complex graph structures; Causal Inference and Treatment Effect Estimation bridges discovery with downstream estimation tasks (e.g., Heterogeneous Treatment Effects[7]); Application-Driven Causal Discovery applies methods to domains like climate science, healthcare, and urban planning; and Integration with Machine Learning and Representation Learning explores synergies with deep learning and feature extraction techniques. A particularly active line of work centers on aggregation strategies that balance diversity and accuracy when combining outputs from multiple algorithms. Some studies emphasize weighted schemes that adapt to algorithm performance (e.g., Bayesian Ensemble Weights[19]), while others explore voting mechanisms or bootstrap-based aggregation (Bootstrap Aggregation[20]). Voting Ensemble[0] sits squarely within the voting-based aggregation cluster, sharing methodological kinship with Weighted Ensemble Connectivity[11] and Algorithm Selection Evaluation[43], which similarly address how to select or combine heterogeneous discovery methods. The central trade-off across these works involves computational cost versus robustness: simpler voting schemes offer interpretability and speed, whereas more sophisticated weighting or meta-learning approaches promise higher accuracy at the expense of complexity. Open questions include how to handle algorithm disagreement, scale ensemble methods to high-dimensional settings, and integrate domain knowledge into aggregation rules.

Claimed Contributions

Principled voting-based framework for structural ensembling with theoretical guarantees

The authors propose a voting-theoretic framework for aggregating multiple causal graph predictions from heterogeneous algorithms. They establish formal conditions under which the ensemble recovers the true causal structure, providing theoretical guarantees that existing heuristic methods lack.

7 retrieved papers
Theoretically justified weighted voting mechanism informed by ensemble design factors

The work derives a Bayes voting rule with theoretical justification for weighting experts. The analysis provides principled guidance on how to configure ensemble parameters such as the number of experts, their competency levels, and diversity to optimize performance.

1 retrieved paper
Parameter estimation framework using optimal transport for noisy expert competencies

The authors develop a parameter estimation method based on optimal transport theory to estimate expert competence transition matrices and priors from noisy graph predictions. They establish consistency guarantees and identifiability conditions for this estimation approach.

0 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Principled voting-based framework for structural ensembling with theoretical guarantees

The authors propose a voting-theoretic framework for aggregating multiple causal graph predictions from heterogeneous algorithms. They establish formal conditions under which the ensemble recovers the true causal structure, providing theoretical guarantees that existing heuristic methods lack.

Contribution

Theoretically justified weighted voting mechanism informed by ensemble design factors

The work derives a Bayes voting rule with theoretical justification for weighting experts. The analysis provides principled guidance on how to configure ensemble parameters such as the number of experts, their competency levels, and diversity to optimize performance.

Contribution

Parameter estimation framework using optimal transport for noisy expert competencies

The authors develop a parameter estimation method based on optimal transport theory to estimate expert competence transition matrices and priors from noisy graph predictions. They establish consistency guarantees and identifiability conditions for this estimation approach.