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A bit confusing is that in the intro, it is stated that f: Xset --> Yset, where Yset = {-1; 1}, while later on, also 0 is in the range of f and I suspect (I am not an expert) that in general f can take real values. Maybe some expert can clarify this in the text?
Moreover, further down, in Eq. (2), another function f appears - this time of a variable eta (instead of xvec) with a different meaning (auxiliary function for the loss function instead of the classifier function) and a different domain than Xset. I propose to replace this (or the f of the classifier) by another letter like g.
Could somebody add a discussion how exactly a scoring rule differs from what is written here?[edit]