A Polynomial Chaos Framework for Causal Discovery in Nonlinear Uncertain Systems

In safety-critical industrial applications, accurately identifying causal relationships and quantifying uncertainty is essential for tasks such as root cause analysis, feature selection, and process optimization. Traditional causal discovery methods inadequately handle nonlinearities and complex uncertainties prevalent in industrial sensor data. To address this, we introduce a novel causal discovery framework that integrates Polynomial Chaos Expansion (PCE) representations of stochastic noise into structural equations. This method effectively captures complex nonlinear couplings and arbitrary noise distributions characteristic of industrial data. We rigorously prove the identifiability of causal structures under mild sparsity conditions on the chaos coefficients, significantly extending classical linear non-Gaussian acyclic model (LiNGAM) identifiability results. Extensive experiments on real-world industrial dataset demonstrate superior accuracy, robustness under extreme non-Gaussian noise conditions, and practical uncertainty quantification. This framework presents a principled, interpretable, and computationally feasible approach to causal analysis in nonlinear uncertain industrial environments.