This seems to ask the question ‘Is a change in the quality of x like colour actually causal to outcomes y?’
Yes, I think you are right. Usually when modeling you can learn correlations that are useful for predictions but if the correlations are spurious they might disappear when the distributions changes. As such to know if p(y|x) changes from only observing x, then we would probably need that all causal relationships to y are captured in x?
Good catch
Yes, I think you are right. Usually when modeling you can learn correlations that are useful for predictions but if the correlations are spurious they might disappear when the distributions changes. As such to know if p(y|x) changes from only observing x, then we would probably need that all causal relationships to y are captured in x?