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

TL;DR

This paper explores the limitations of current causal discovery algorithms, emphasizing the importance of emergent causes and proposing updates to better detect complex causal influences beyond pairwise interactions.

Contribution

It demonstrates that causal emergent information resides in CMIs and suggests modifications to causal discovery algorithms to identify emergent causal influences.

Findings

Causal emergent information is contained in CMIs.

Violations of faithfulness can occur without pairwise interactions.

Updated algorithms can detect emergent causal influences.

Abstract

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.