Feedback on first draft.
Looks good. Here are a few comments based on the first draft.
In preliminaries, what are the "responses"? Why do you say ? is the missing entries inside X, but then also use it for y in your example? (Does it mean something different there?)
What is a missingness indicator for a feature? (What does a feature missing mean, when the feature can be missing for some examples and not for others? What if every feature has at least one example with that feature missing?
I'm not sure it is appropriate to claim that women are less likely to reveal their age (even if it were true).
I cannot work out from your examples what the difference between MAR and NMAR. (I guess that MCAR is when R variable has no parents). Why isn't there a gender variable as well as a GENDER variable? I'm guessing that this means that gender is not observed. In the description how does "using another method" relate to "model why the data are missing"? Is there a clearer definition?
Why is collaborative filtering suitable for NMAR?
I am not sure what "complete training data, incomplete test data" - isn't this what supervised machine learning is? I thought that you were considering missing data in the training set (that is what I got from the introduction, which I thought was all about the training data).