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Second-Order Taylor Expansion of Wasserstein Metric and Related Metrics
Suppose that we have a parametric distribution $P_{\theta}$, which is indexed by the parameter $\theta \in \mathbb{R}^d$. Let $W\{\cdot,\cdot\}$ be the Wasserstein Metric between two distributions.
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Empirical estimation of $\inf_{\gamma \in \Pi(\mu,\nu)}\gamma(\Omega)$, given i.i.d samples from $\mu$ and $\nu$
Let $\mathcal X$ be a Polish space and $\Omega \subseteq \mathcal X^2$ be open. Let $\mu$ and $\nu$ be probability measures, and consider the quantity $c_\Omega(\mu,\nu)$ defined by
$$
c_\Omega(\mu,\...
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