CausalMorph: Preconditioning data for linear non-Gaussian acyclic models

• Introduction of CausalMorph , a three-stage algorithm that projects observational data toward the regime assumed by Linear Non-Gaussian Acyclic Models (LiNGAM). • Application of CausalMorph to 17,280 unique data configurations results in a significant 37.7% relative reduction in Structural Hamming Distance (SHD) for downstream DirectLiNGAM ( p < .001). • Evidience of a regularization effect is found, with improved causal discovery accuracy even under ideal LiNGAM conditions, indicating mitigation of finite-sample artifacts. • Provides evidence for data projection as a practical strategy for extending the applicability of the LiNGAM framework. Moving from associative learning to inferring cause–effect relationships remains a central challenge for intelligent systems. The Linear Non-Gaussian Acyclic Model (LiNGAM) family identifies a single, fully directed causal graph from observational data rather than an equivalence class. However, deviations from its assumptions of linearity and non-Gaussian noise limit its applicability. To address this, this paper introduces CausalMorph, a data preconditioning algorithm that projects observational data toward a regime compatible with LiNGAM. The projection employs a three-stage sequence: local linearization of causal mechanisms, synthesis of non-Gaussian residuals, and orthogonalization of parent-residual dependencies. Across an evaluation of 34,560 synthetic paired experiments, CausalMorph yielded significant reductions in Structural Hamming Distance (SHD) of 37.7% ± 10.8% for DirectLiNGAM and 16.4% ± 13.8% for ICA-LiNGAM ( p < 0.001). Additionally, the CausalMorph + DirectLiNGAM pipeline achieved a lower mean SHD than the differentiable non-linear baseline algorithm in both linear and non-linear regimes. By operating as a non-iterative, single-pass projection, the method avoids the k iter optimization loops required by continuous frameworks, offering a highly efficient path to structural recovery. The algorithm also systematically rescues baseline solvers from catastrophic large-sample traps under fully Gaussian noise, and maintains an 85.8% win rate over the baseline when utilizing an autonomous data-driven initialization for the prior causal order. These findings suggest statistical projection as a viable and structurally conservative strategy for applying LiNGAM-based causal discovery to data environments that violate its base assumptions.