## New answers tagged it.information-theory

1
vote

### Riemannian submanifolds of $2$-Wasserstein space

Other than point masses in a length space or Gaussian measures in $\mathbb{R}^n$, I don't know of examples of families which are totally geodesic in Wasserstein geometry.
However, it is possible to ...

2
votes

Accepted

### Reverse Pinsker's inequality for smooth density classes

The answer is no.
E.g., suppose that both $f$ and $g$ are supported on $B=[0,1]$, with $f=1$ on $B$ and
$$g(x)=(1-h+x)\,1(0\le x<h)+1(h\le x<1-h)+(x+h)\,1(1-h\le x\le1)$$
for $h\in(0,1/2)$ and $...

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