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Learning Dynamic Causal Graphs Under Parametric Uncertainty via Polynomial Chaos Expansions

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Causal DiscoveryPolynomial Chaos ExpansionParametric UncertaintyFunctional Causal ModelsUncertainty Quantification
Abstract:

Existing causal discovery methods are fundamentally limited by the assumption of a static causal graph, a constraint that fails in real-world systems where causal relationships dynamically vary with underlying system parameters. This discrepancy prevents the application of causal discovery in critical domains such as industrial process control, where understanding how causal effects change is essential. We address this gap by proposing a new paradigm that moves beyond static graphs to learn functional causal representations. We introduce a framework that models each causal link not as a static weight but as a function of measurable system parameters. By representing these functions using Polynomial Chaos Expansions (PCE), we develop a tractable method to learn the complete parametric causal structure from observational data. We provide theoretical proofs for the identifiability of these functional models and introduce a novel, provably convergent learning algorithm. On a large-scale chemical reactor dataset, our method learns the dynamic causal structure with a 90.9% F1-score, nearly doubling the performance of state-of-the-art baselines and providing an interpretable model of how causal mechanisms evolve.

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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.
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Overview

Overall Novelty Assessment

The paper proposes a framework for learning functional causal representations where each causal link is modeled as a function of measurable system parameters, using Polynomial Chaos Expansions for tractability. It resides in the 'Parametric and Functional Causal Models' leaf, which contains only two papers total. This is a notably sparse research direction within the broader taxonomy of fifty papers, suggesting the specific combination of functional causal modeling with parametric uncertainty remains relatively unexplored compared to neighboring areas like Dynamic Bayesian Networks or Time-Varying Parameter Models.

The taxonomy reveals several related but distinct research directions. The sibling leaf 'Nonparametric Causal Discovery' focuses on latent variables and distribution-free approaches without explicit functional forms. Nearby branches include 'Dynamic Bayesian Networks' with probabilistic temporal dependencies and 'Time-Varying Parameter Models' addressing parameter drift in forecasting contexts. The paper's approach diverges by explicitly modeling causal links as parameter-dependent functions rather than treating parameters as latent states or time-indexed coefficients, positioning it at the intersection of structural causal discovery and parametric modeling.

Among twenty candidates examined across three contributions, no clearly refuting prior work was identified. The functional causal representation framework examined three candidates with zero refutations, the PCT-CD algorithm examined seven candidates with zero refutations, and the theoretical convergence guarantees examined ten candidates with zero refutations. This suggests that within the limited search scope, the specific combination of functional causal modeling, PCE-based representations, and identifiability proofs for parameter-dependent structures appears relatively novel, though the search scale precludes definitive claims about the broader literature.

Based on top-twenty semantic matches and the sparse taxonomy leaf, the work appears to occupy a distinct niche combining causal discovery with parametric functional modeling. The analysis covers closely related methods in causal structure learning and temporal modeling but does not exhaustively survey all parametric uncertainty literature or industrial process control applications, which may contain relevant domain-specific approaches not captured in this search.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
20
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: learning dynamic causal graphs under parametric uncertainty. The field addresses how causal relationships evolve over time when model parameters themselves are uncertain or changing. The taxonomy reveals several complementary perspectives: one branch focuses on Causal Graph Structure Learning and Identifiability, examining foundational questions about when and how causal structures can be uniquely recovered from data, including parametric and functional models such as Nonadditive Causal Identifiability[1]. Another branch emphasizes Bayesian Network Inference and Dynamic Modeling, leveraging probabilistic frameworks like Learning Dynamic Bayesian[8] networks to handle temporal dependencies and uncertainty propagation. Temporal Causal Modeling and Reasoning explores methods for tracking causality across time, as seen in Temporal Causal Inference[2] and works on uncertain temporal graphs[23]. Time-Varying Parameter Models and Forecasting tackle scenarios where parameters drift or shift, exemplified by Bayesian Structural Timeseries[15] and Timevarying Structural VAR[38]. Graph Neural Networks for Spatiotemporal Causal Modeling apply deep learning architectures to capture complex spatial and temporal patterns, while Application Domains and Specialized Methods demonstrate how these techniques solve real-world problems in healthcare, finance, and industrial diagnostics. A particularly active line of work centers on parametric and functional causal models, where researchers grapple with identifiability under nonstandard assumptions and evolving structures. Dynamic Causal Graphs[0] sits squarely within this branch, addressing the challenge of inferring causal graphs when both structure and parameters change over time. Its emphasis on parametric uncertainty distinguishes it from nearby efforts like Nonadditive Causal Identifiability[1], which focuses on static identifiability conditions under nonadditive noise, and Temporal Causal Inference[2], which prioritizes temporal reasoning without explicit parametric drift modeling. Meanwhile, Bayesian approaches such as Variational Bayesian Causal[32] and Dynamic Bayesian Networks[28] offer complementary probabilistic machinery for uncertainty quantification, though they often assume fixed or slowly varying structures. Open questions remain about scalability, the trade-off between model flexibility and identifiability guarantees, and how to integrate domain knowledge when parameters exhibit abrupt regime changes.

Claimed Contributions

Functional causal representation framework with identifiability guarantees

The authors formalize an industrial structural causal model where edge weights are explicit functions of operating conditions rather than static values. They prove identifiability of these parametric mechanisms under mild assumptions, establishing that the DAG and parameter-dependent functions can be uniquely recovered from observational data.

3 retrieved papers
PCT-CD algorithm for parametric causal discovery

The authors develop an end-to-end algorithm that uses Polynomial Chaos Expansions to represent causal functions, introduces a novel conditional independence test tailored to parametric uncertainty, and employs natural gradient optimization for score-based refinement. The method learns complete parametric causal structures from observational data.

7 retrieved papers
Theoretical convergence and sample complexity guarantees

The authors establish finite-sample guarantees for graph recovery, proving consistency of coefficient estimators and deriving explicit sample complexity bounds. They also prove linear convergence of the natural gradient descent procedure used in the optimization phase.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Functional causal representation framework with identifiability guarantees

The authors formalize an industrial structural causal model where edge weights are explicit functions of operating conditions rather than static values. They prove identifiability of these parametric mechanisms under mild assumptions, establishing that the DAG and parameter-dependent functions can be uniquely recovered from observational data.

Contribution

PCT-CD algorithm for parametric causal discovery

The authors develop an end-to-end algorithm that uses Polynomial Chaos Expansions to represent causal functions, introduces a novel conditional independence test tailored to parametric uncertainty, and employs natural gradient optimization for score-based refinement. The method learns complete parametric causal structures from observational data.

Contribution

Theoretical convergence and sample complexity guarantees

The authors establish finite-sample guarantees for graph recovery, proving consistency of coefficient estimators and deriving explicit sample complexity bounds. They also prove linear convergence of the natural gradient descent procedure used in the optimization phase.

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