摘要：Given two probability measures, $\mathbb{P}$ and $\mathbb{Q}$ defined on a measurable space, $S$, the integral probability metric (IPM) is defined as $$\gamma_{\EuScript{F}}(\mathbb{P},\mathbb{Q})=\sup\left\{\left\vert \int_{S}f\,d\mathbb{P}-\int_{S}f\,d\mathbb{Q}\right\vert\,:\,f\in\EuScript{F}\right\},$$ where $\EuScript{F}$ is a class of real-valued bounded measurable functions on $S$. By appropriately choosing $\EuScript{F}$, various popular distances between $\mathbb{P}$ and $\mathbb{Q}$, including the Kantorovich metric, Fortet-Mourier metric, dual-bounded Lipschitz distance (also called the Dudley metric), total variation distance, and kernel distance, can be obtained.
