  The relationship between statistical dependency and causality lies at the
heart of all statistical approaches to causal inference. Recent results in the
ChaLearn cause-effect pair challenge have shown that causal directionality can
be inferred with good accuracy also in Markov indistinguishable configurations
thanks to data driven approaches. This paper proposes a supervised machine
learning approach to infer the existence of a directed causal link between two
variables in multivariate settings with $n>2$ variables. The approach relies on
the asymmetry of some conditional (in)dependence relations between the members
of the Markov blankets of two variables causally connected. Our results show
that supervised learning methods may be successfully used to extract causal
information on the basis of asymmetric statistical descriptors also for $n>2$
variate distributions.
