Information-theoretic causal discovery

In this dissertation, we aim to alleviate some of the weaknesses of constraint-based algorithms. In the first part, we investigate causal mechanisms, which cannot be detected when assuming faithfulness. We then suggest a weaker assumption based on triple interactions, which allows for recovering a broader spectrum of causal mechanisms. Subsequently, we focus on conditional independence testing, which is a crucial tool for causal discovery. In particular, we propose to measure dependencies through conditional mutual information, which we show can be consistently estimated even for the most general setup: discrete-continuous mixture random variables. Last, we focus on distinguishing Markov equivalent graphs (i.e. infer the complete DAG structure), which boils down to inferring the causal direction between two random variables. In this setting, we focus on continuous and mixed-type data and develop our methods based on an information-theoretic postulate, which states that the true causal graph can be compressed best, i.e. has the smallest Kolmogorov complexity.

Die Arbeit wurde von Prof. Dr. Jilles Vreeken betreut.