  Built upon the concept of causal faithfulness, the so-called causal discovery
algorithms propose the breakdown of mutual information (MI) and conditional
mutual information (CMI) into sets of variables to reveal causal influences.
These algorithms suffer from the lack of accounting emergent causes when
connecting links, resulting in a spuriously embellished view of the
organization of complex systems. Here, we show that causal emergent information
is necessarily contained in CMIs. We also connect this result with the
intrinsic violation of faithfulness and elucidate the importance of the concept
of causal minimality. Finally, we show how faithfulness can be wrongly assumed
only because of the appearance of spurious correlations by providing an example
of a non-pairwise systems which should violate faithfulness, in principle, but
it does not. The net result proposes an update to causal discovery algorithms,
which can, in principle, detect and isolate emergent causal influences in the
network reconstruction problems undetected so far.
