Hessian输运梯度流

摘要：

我们得到了新的梯度流的发散函数的概率空间中嵌入一类黎曼度量。黎曼度量张量是从熵函数的迁移海森算子建立的。新的梯度流是一个广义Fokker-Planck方程，并与一个随机微分方程，依赖于参考措施。Hessian输运梯度流和相关的随机微分方程的几个例子，包括反向Kullback-Leibler发散，α发散，Hellinger距离，皮尔逊发散，和Jenson-Shannon发散。

英文摘要：

We derive new gradient flows of divergence functions in the probability space embedded with a class of Riemannian metrics. The Riemannian metric tensor is built from the transported Hessian operator of an entropy function. The new gradient flow is a generalized Fokker-Planck equation and is associated with a stochastic differential equation that depends on the reference measure. Several examples of Hessian transport gradient flows and the associated stochastic differential equations are presented, including the ones for the reverse Kullback--Leibler divergence, alpha-divergence, Hellinger distance, Pearson divergence, and Jenson--Shannon divergence.

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。