论文标题
在瓦斯堡空间上快速而光滑的插值
Fast and Smooth Interpolation on Wasserstein Space
论文作者
论文摘要
我们提出了一种使用最佳传输几何形状平滑插值概率度量的新方法。为此，我们将这个问题减少到经典的欧几里得设置，从而使我们能够直接利用样条插值的广泛工具箱。与以前的测量配置条的方法不同，我们的插值曲线（i）具有明确的解释为管理粒子流，这对于应用是自然的，并且（ii）在Wasserstein空间上提供了第一个近似保证。最后，我们通过使用薄板花键拟合度量的表面来证明我们的插值方法的广泛适用性。
We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox of spline interpolation. Unlike previous approaches to measure-valued splines, our interpolated curves (i) have a clear interpretation as governing particle flows, which is natural for applications, and (ii) come with the first approximation guarantees on Wasserstein space. Finally, we demonstrate the broad applicability of our interpolation methodology by fitting surfaces of measures using thin-plate splines.
