Plugin estimation of smooth optimal transport maps
光滑最优输运映射的插件估计
We analyze a number of natural estimators for the optimal transport map between two distributions and show that they are minimax optimal. We adopt the plugin approach: our estimators are simply optimal couplings between measures derived from our observations, appropriately extended so that they define functions on Rd. When the underlying map is assumed to be Lipschitz, we show that computing the optimal coupling between the empirical measures, and extending it using linear…