General power laws of the causalities in the causal Bayesian networks

Abstract

The power laws of network geometric properties are widely adopted to characterize the critical phenomena of complex systems, which may not describe the diverse interactions in systems effectively. By comparison, the causality represents the complicated interactions. Therefore, in this work, the power law of the causal effects in systems is studied to reflect the critical states from the perspective of causality. The causal Bayesian networks and effective information are adopted to construct the causal relationships and quantify the causal effects. The study on 20 systems from different fields shows that for a considerable proportion of systems, the causal effects of the factors in systems follow the power laws. For such causal power laws, an explanation based on the principle of maximum entropy is proposed and verified. The causal power laws may imply some critical states of systems, and can provide the basis for the quantification of systems’ states and functions.

KEYWORDS:

• Causal effect
• power law
• structural causal model
• causal Bayesian network
• effective information
• maximum entropy

Data availability statement

The data of systems studied in this work can be referred to the corresponding citations.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 51775020]; the National Natural Science Foundation of China [grant number 62073009]; and the Beijing Natural Science Foundation of China [grant number 7222086].