Distinguishing between cause and effect: estimation of causal graphs with two variables

In causal discovery, one is given a joint distribution and tries to infer the causal graph of the underlying data generating process. The case of two variables is particularly challenging since no conditional independences between the variables can be exploited. We review different methods that suggest solutions for this problem and investigate the so-called additive noise models in more detail. We further show a second reason for the importance of bivariate models. Under suitable conditions model classes that can distinguish between cause and effect can be used to identify causal graphs with any finite number of nodes.