嵌套Sinkhorn发散计算嵌套距离
Nested Sinkhorn Divergence To Compute The Nested Distance
摘要：
嵌套距离建立在Wasserstein距离的基础上，以量化随机过程的差异，包括通过过滤建模的信息。Sinkhorn散度是Wasserstein距离的一种松弛，可以更快地计算。为此，我们采用Sinkhorn发散，并利用相关的（不动点）迭代算法。此外，我们调查整个阶段的随机过程的熵的过渡，并提供了一个熵正则化的嵌套距离公式，包括其对偶的表征。数值实验证实了计算的优势和优越性。
英文摘要：
The nested distance builds on the Wasserstein distance to quantify the difference of stochastic processes, including also the information modelled by filtrations. The Sinkhorn divergence is a relaxation of the Wasserstein distance, which can be computed considerably faster. For this reason we employ the Sinkhorn divergence and take advantage of the related (fixed point) iteration algorithm. Furthermore, we investigate the transition of the entropy throughout the stages of the stochastic process and provide an entropy-regularized nested distance formulation, including a characterization of its dual. Numerical experiments affirm the computational advantage and supremacy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
