Efficient Identification of Causal Effects

Investigating causality and causal effects has been the primary aim of all natural sciences but for a long time there was no clear definition of causality and no sound formalism to reason about causality. Judea Pearl's seminal work on causality provides the mathematical foundations of causality by combining the fields of graph theory and statistics. Pearl describes the reasoning about causality as reasoning about the effects of interventions, such that a causal model quantitatively predicts the statistical implications and causal effects of interventions.In a confirmatory (or theory-driven) approach, one starts from a certain causal model and predicts the outcome of experiments.In an exploratory (or data-driven) approach, one starts from data or experiments and learns a causal model that could have generated this data. Our goal is to combine these two kinds of approaches to identify causal effects that could not be identified directly from either causal model or the experiments alone.Another area of interest are linear causal models, which are perhaps the most commonly used models in practice. There the direct causal effect of one variable on another is a single parameter, so algebraic methods can be applied to identify it. We plan to investigate on which graphs this identification succeeds.Finally, we plan to investigate pattern matching on the graph to recognize certain causal structures, and apply our results to practical data.