Learning causal structures plays an important role in various fields, ranging from biology and clinical medicine to economics and many others. Since using controlled experiments is often not possible due to cost or ethical reasons, causal discovery based on only observational data is an interesting topic of research. In order to study causal structures researchers often employ Structural Equation Models (SEM). In general, the true underlying causal structure cannot be uniquely identified. To avoid this problem, constrained version of SEM’s can be considered. However, if we would like to have a flexible model which can describe data generation process in real life, the constraints should not be too strict. Post-Nonlinear (PNL) causal models are quite general form of SEM’s, which include many other models discussed in the literature, such as Linear SEM’s and Additive Noise Models. This thesis studies both bivariate and multivariate PNL models under the assumption of Gaussian noise. We employ Linear Transformation Models and estimate the involved parameters with Pairwise-Rank likelihood methods. Furthermore, we prove asymptotic normality and consistency of our proposed estimates. Using those results, we developed computationally fast algorithms to estimate the causal ordering within PNL models and prove consistency with high probability. The performance of our method is evaluated on simulated data. At the end, general PNL models (not necessarily with Gaussian noise) have been discussed by showing how the same ideas can be transferred to general models.      «

Learning causal structures plays an important role in various fields, ranging from biology and clinical medicine to economics and many others. Since using controlled experiments is often not possible due to cost or ethical reasons, causal discovery based on only observational data is an interesting topic of research. In order to study causal structures researchers often employ Structural Equation Models (SEM). In general, the true underlying causal structure cannot be uniquely identified. To avo...     »