  Knowing the features of a complex system that are highly relevant to a
particular target variable is of fundamental interest in many areas of science.
Existing approaches are often limited to linear settings, sometimes lack
guarantees, and in most cases, do not scale to the problem at hand, in
particular to images. We propose DRCFS, a doubly robust feature selection
method for identifying the causal features even in nonlinear and high
dimensional settings. We provide theoretical guarantees, illustrate necessary
conditions for our assumptions, and perform extensive experiments across a wide
range of simulated and semi-synthetic datasets. DRCFS significantly outperforms
existing state-of-the-art methods, selecting robust features even in
challenging highly non-linear and high-dimensional problems.
