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

Shaking the causal tree: On the faithfulness and minimality assumptions beyond pairwise interactions