Causal statistical inference in high dimensions

We present a short selective review of causal inference from observational data, with a particular emphasis on the high-dimensional scenario where the number of measured variables may be much larger than sample size. Despite major identifiability problems, making causal inference from observational data very ill-posed, we outline a methodology providing useful bounds for causal effects. Furthermore, we discuss open problems in optimization, non-linear estimation and for assigning statistical measures of uncertainty, and we illustrate the benefits and limitations of high-dimensional causal inference for biological applications. Copyright Springer-Verlag 2013