We can then study the minimax risk of sampling , M I ( F G , , n ) : = inf X sup P ∈F G R I ( P , X ) . A few remarks about M I ( F , , n ): First , we implicitly assumed ( P , P X(X1 : n , Z)|X1 : n ) is well - defined , which is not obvious unless P X(X1 : n , Z ) ∈ F G . We discuss this assumption further below . Second , since the risk R I ( P , X ) depends on the unknown true distribution P , we can not calculate it in practice . Third , for the same reason ( because R P ( P , X ) depends directly on P rather than particular data X 1 : n ) , it detect lack - of - diversity issues such as mode collapse . As we discuss in the Appendix , these latter two points are distinctions from the recent work of [ 7 ] on generalization in GANs .