Causal Structure Learning and Effect Identification in Linear Non-Gaussian Models and Beyond

In many fields of science, researchers are keen to learn causal connections among quantities of interest. For instance, in medical studies doctors want to infer the effect of a new drug on the recovery from a particular disease, or economists may be interested in the effect of education on income.

The preferred approach to causal inference is to carry out controlled experiments. However, such experiments are not always possible due to ethical, financial or technical restrictions. An important problem is thus the development of methods to infer cause-effect relationships from passive observational data. While this is a rather old problem, in the late 1980s research on this issue gained significant momentum, and much attention has been devoted to this problem ever since. One rather recently introduced framework for causal discovery is given by linear non-Gaussian acyclic models (LiNGAM). In this thesis, we apply and extend this model in several directions, also considering extensions to non-parametric acyclic models.

We address the problem of causal structure learning from time series data, and apply a recently developed method using the LiNGAM approach to two economic time series data sets. As an extension of this algorithm, in order to allow for non-linear relationships and latent variables in time series models, we adapt the well-known Fast Causal Inference (FCI) algorithm to such models.

We are also concerned with non-temporal data, generalizing the LiNGAM model in several ways: We introduce an algorithm to learn the causal structure among multidimensional variables, and provide a method to find pairwise causal relationships in LiNGAM models with latent variables. Finally, we address the problem of inferring the causal effect of one given variable on another in the presence of latent variables. We first suggest an algorithm in the setting of LiNGAM models, and then introduce a procedure for models without parametric restrictions.

Overall, this work provides practitioners with a set of new tools for discovering causal information from passive observational data in a variety of settings.