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<p>We propose a non-linear extension of the Linear Non-Gaussian Acyclic Model (LiNGAM) for causal discovery. For each variable, the method fits a penalized additive regression on the other variables and uses the Hilbert–Schmidt Independence Criterion (HSIC) to test whether the residuals depend on a predictor omitted from the fit. Residual dependence on the omitted predictor indicates an edge between the two variables, and the larger of the two HSIC scores identifies the parent. Pairwise HSIC tests therefore recover the causal edges under Benjamini–Hochberg control of the false discovery rate. Under smooth additive structural equations with mutually independent, non-Gaussian noise, the method consistently recovers the causal graph in polynomial time. In the linear case, its residual diagnostics match those of LiNGAM. For each selected edge, the method also yields a fitted partial effect curve, an interpretable summary of how the parent influences the child. Simulations confirm the recovery guarantee at finite samples, and on a wine chemistry dataset the recovered curves agree with the wine-chemistry literature without assuming a specific functional form.</p>

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Non-linear causal inference in observational data using additive models and kernel-based independence testing

  • 期刊论文

  • 发表日期：

    2026年5月27日

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  • Ashraful Islam,
  • Joe Suzuki

摘要

We propose a non-linear extension of the Linear Non-Gaussian Acyclic Model (LiNGAM) for causal discovery. For each variable, the method fits a penalized additive regression on the other variables and uses the Hilbert–Schmidt Independence Criterion (HSIC) to test whether the residuals depend on a predictor omitted from the fit. Residual dependence on the omitted predictor indicates an edge between the two variables, and the larger of the two HSIC scores identifies the parent. Pairwise HSIC tests therefore recover the causal edges under Benjamini–Hochberg control of the false discovery rate. Under smooth additive structural equations with mutually independent, non-Gaussian noise, the method consistently recovers the causal graph in polynomial time. In the linear case, its residual diagnostics match those of LiNGAM. For each selected edge, the method also yields a fitted partial effect curve, an interpretable summary of how the parent influences the child. Simulations confirm the recovery guarantee at finite samples, and on a wine chemistry dataset the recovered curves agree with the wine-chemistry literature without assuming a specific functional form.