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.