4

Wasserstein distance between two gaussians has a well known closed form solution. Does the same hold for the distance between a Gaussian with a fixed variance(say 1) and the empirical data distribution?

Empirical data distibution defined as: $$ p(x) = \frac{\sum_i \delta (x - x_i)}{n} $$

And the 1-d Gaussian with $\sigma^2 = 1$ and some unknown mean $\mu$ $$ q(x) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}} $$

user3838440
  • 41
  • 1
  • See equation 2 of https://arxiv.org/pdf/1507.04090.pdf or equation 1.3 of https://arxiv.org/pdf/1503.00113.pdf . Maybe not "closed-form", but can be numerically evaluated. – Mark L. Stone May 02 '18 at 01:03

0 Answers0