In this paper, a new metric was proposed to evaluate generative model.
The equation (1) decomposes generative distribution and real distribution into two parts w.r.t their intersection of the supports.
Then he demonstrated the case that the distribution on the support $S$ is equal with pictures (a)-(d) in Figure 2.
My first question:
In the picture (a), the distribution $P$ has two modes, and $Q$ has one mode but higher than $P$. Why they have same distribution over the $S$?
Then, the author discussed the case when the distribution over $S$ are different and he decomposed the distribution similarly like above.
And the define a PRD function in definition 2.
My second question is that after my generative model was trained, its distribution was determined. When two distribution were given, shouldn't the alpha and beta be constants? Why in the definition said "all (alpha,beta) satisfying definition 1"?