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response variable at the group level, independent variables at the entity level

I have a dataset of entities which each belong to a particular group (i.e. entity=schools and group=school district). I also have lots of auxiliary variables on each entity. However, for my response ...
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How to understand the definition of Greedy Target-based Statistics in the CatBoost paper

There is a method named Target statistics to deal with categorical features in the catboost paper. I still some confusion about the mathematical form. Could you some guys to expain how to compute it! $...