Here are some examples of the methods that exploit the independence between cause and mechanism:
 - NonLinear Deterministic Mechanism
 - Unsupervised Inverse Regression
 - Causal Inference via Kernel Deviance Measures
 - Cause-Effect Inference by Comparing Regression Errors

University of Michigan - Ann Arbor

This class of methods exploits the notion of complexity of the causal mechanisms from a different perspective. They are based on the principle saying that when X → Y the distribution of the cause $P_X$ should not contain information that can be useful to derive the conditional model $Q_{Y | X}$ on the data.

Methods Exploiting the Independence between Cause and Mechanism

 Isabelle Guyon, Alexander Statnikov, Berna Bakir Batu (2019)
Cause Effect Pairs in Machine Learning (The Springer Series on Challenges in Machine Learning)
https://www.amazon.com/Effect-Machine-Learning-Springer-Challenges/dp/3030218090

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