  The problem of inferring the direct causal parents of a response variable
among a large set of explanatory variables is of high practical importance in
many disciplines. Recent work exploits stability of regression coefficients or
invariance properties of models across different experimental conditions for
reconstructing the full causal graph. These approaches generally do not scale
well with the number of the explanatory variables and are difficult to extend
to nonlinear relationships. Contrary to existing work, we propose an approach
which even works for observational data alone, while still offering theoretical
guarantees including the case of partially nonlinear relationships. Our
algorithm requires only one estimation for each variable and in our experiments
we apply our causal discovery algorithm even to large graphs, demonstrating
significant improvements compared to well established approaches.
