I am part of the Causal and Probabilistic Inference Group and I am working on the problem of inferring causal relations in cases where interventions are infeasible and therefore only data from passive observations is available. It has been argued that causal information can be obtained from statistical conditional independences through the so called Causal Markov and Faithfulness conditions. However, there exist two limitations in this approach. First, inferences can only be drawn in the case of more than two variables. Therefore we are searching for additional assumptions that allow for conclusions already in the two variable case. Second, estimating conditional dependences is challenging if only a limited number of samples are at hand or if samples cannot be obtained under similar experimental conditions (non-i.i.d). We addressed this issue by considering not only statistical but also algorithmic notions of dependences based on the framework of algorithmic information theory. Since the latter rests upon Kolmogorov complexity that is uncomputable we are working on a formal framework for computable alternatives.