Assumptions in causal machine learning I am currently reading about causal machine learning, e.g. causal bayesian networks.
I am wondering about the assumptions on that the causal machine learning models are based. For example, for linear regression the error term needs to be uncorrelated with the regressors so that the effect of the regressors on y is unbiased. I have not read about any such assumptions for a causal bayesian network.
What if there is a hidden variable that is in fact part of the network, but is not represented in the data. Can the results of a causal bayesian network analysis be still called causal? Can you redirect me to some good books, where assumption of causal machine learning are made more clear.
 A: The article from Pearl on The seven tools of causal inference, with reflections on Machine Learning is probably a concise enough intro to get you started. In a way, I would suggest ignoring the "ML" part of your question and first focusing on the "Causal" part. The principles will be the same and ML, isn't a panacea, if our causal assumptions are violated when using a "simple Stats" model, using an "advanced ML" model will fail just as well.
Starting off with Cunningham's The Mixtape book or Huntington-Klein's The Effect book would be suitable suggestions for a new starter. (Both books are free online too.) For something more formal would be the What If book from Hernan & Robins and Elements of causal inference by Peters et al.  These four freely available books would most likely cover the vast majority of CI use cases one come across.
A: There are no general assumptions, it's just that, the fewer assumptions you are willing to make, the more difficult it gets.
In the same way, as there are different methods to do linear regression under many different conditions, including the situation that errors do depend on the regressor, there are many different methods to do causal analysis under different presumptions.
Thus, there are different methods for the situation that hidden confounders are present (your example) or that there is selection bias or that causal loops are possible.
A good introductory book is

Peters, Jonas, Dominik Janzing, and Bernhard Schölkopf. Elements of causal inference: foundations and learning algorithms. The MIT Press, 2017.

