We consider the problem of inferring the directed, causal graph from
observational data, assuming no hidden confounders. We take an information
theoretic approach, and make three main contributions...
First, we show how through algorithmic information theory we can obtain SCI,
a highly robust, effective and computationally efficient test for conditional
independence---and show it outperforms the state of the art when applied in
constraint-based inference methods such as stable PC. Second, building upon on SCI, we show how to tell apart the parents and
children of a given node based on the algorithmic Markov condition. We give the
Climb algorithm to efficiently discover the directed, causal Markov
blanket---and show it is at least as accurate as inferring the global network,
while being much more efficient. Last, but not least, we detail how we can use the Climb score to direct those
edges that state of the art causal discovery algorithms based on PC or GES
leave undirected---and show this improves their precision, recall and F1 scores
by up to 20%.