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.

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.

