  Discovering the causal structure among a set of variables is a fundamental
problem in many areas of science. In this paper, we propose Kernel Conditional
Deviance for Causal Inference (KCDC) a fully nonparametric causal discovery
method based on purely observational data. From a novel interpretation of the
notion of asymmetry between cause and effect, we derive a corresponding
asymmetry measure using the framework of reproducing kernel Hilbert spaces.
Based on this, we propose three decision rules for causal discovery. We
demonstrate the wide applicability of our method across a range of diverse
synthetic datasets. Furthermore, we test our method on real-world time series
data and the real-world benchmark dataset Tubingen Cause-Effect Pairs where we
outperform existing state-of-the-art methods.
