Causal models for decision making via integrative inference

Understanding causes and effects is important in many parts of life, especially when decisions have to be made. The systematic inference of causal models remains a challenge though. In this thesis, we study (1) “approximative” and “integrative” inference of causal models and (2) causal models as a basis for decision making in complex systems. By “integrative” here we mean including and combining settings and knowledge beyond the outcome of perfect randomization or pure observation for causal inference, while “approximative” means that the causal model is only constrained but not uniquely identified. As a basis for the study of topics (1) and (2), which are closely related, we first introduce causal models, discuss the meaning of causation and embed the notion of causation into a broader context of other fundamental concepts. Then we begin our main investigation with a focus on topic (1): we consider the problem of causal inference from a non-experimental multivariate time series (Xt)t∈Z, that is, we integrate temporal knowledge. We take the following approach: We assume that (Xt)t∈Z together with some potential hidden common cause – “confounder” – (Zt)t∈Z forms a first order vector autoregressive (VAR) process with structural transition matrix A. Then we examine under which conditions the most important parts of A are identifiable or approximately identifiable from only (Xt)t∈Z, in spite of the effects of (Zt)t∈Z. Essentially, sufficient conditions are (a) non-Gaussian, independent noise or (b) no influence from (Xt)t∈Z to (Zt)t∈Z. We present two estimation algorithms that are tailored towards conditions (a) and (b), respectively, and evaluate them on synthetic and real-world data. We discuss how to check the model using (Xt)t∈Z. Still focusing on topic (1) but already including elements of topic (2), we consider the problem of approximate inference of the causal effect of a variable X on a variable Y in i.i.d. settings “between” randomized experiments and observational studies. Our approach is to first derive approximations (upper/lower bounds) on the causal effect,