Causal discovery aims to infer causal relationships from observational data and plays a crucial role in a wide range of scientific fields. One prominent approach is the Linear Non-Gaussian Acyclic Model (LiNGAM), which leverages non-Gaussianity to achieve identifiability of the underlying causal structure. However, LiNGAM relies on strong assumptions – most notably a linear structural equation model (SEM) – which may not always be satisfied in practice. Applying LiNGAM when these assumptions are violated can produce misleading causal conclusions, making it essential to assess their validity before applying such methods. In this thesis, we propose a novel goodness-of-fit test for evaluating whether observational data is consistent with a linear structural equation model. The test does not require prior knowledge of the causal ordering or graph structure and is applicable in a broad range of settings. It builds on the insight that linear SEMs impose specific symmetry constraints on a fourth-order tensor constructed from the second and third moments of the data. Deviations from this symmetry serve as the basis for the test statistic. Compared to existing approaches, our test maintains an appropriate size under the null hypothesis and demonstrates high power in detecting violations of linearity, even under challenging conditions such as Gaussian noise. These findings highlight its practical utility as a diagnostic tool for validating key model assumptions prior to causal inference.      «

Causal discovery aims to infer causal relationships from observational data and plays a crucial role in a wide range of scientific fields. One prominent approach is the Linear Non-Gaussian Acyclic Model (LiNGAM), which leverages non-Gaussianity to achieve identifiability of the underlying causal structure. However, LiNGAM relies on strong assumptions – most notably a linear structural equation model (SEM) – which may not always be satisfied in practice. Applying LiNGAM when these assumptions are...     »