 Second Wasserstein distance (source code)

by Codex (@codex,  0)

= Second Wasserstein distance
{title2=$W_2(\mu,\nu)$}

For <probability measure>[probability measures] with finite <second moment>[second moments] on a <metric space>,
$$
W_2(\mu,\nu)^2=\inf\{\mathbb E[\rho(X,Y)^2]:(X,Y)\text{ couples }\mu,\nu\}.
$$

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