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.

中文翻译：

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黑森州运输梯度流

我们在嵌入了一类黎曼度量的概率空间中得出了发散函数的新梯度流。黎曼度量张量是根据熵函数的运输的Hessian运算符构建的。新的梯度流是广义的Fokker-Planck方程，并且与依赖于参考度量的随机微分方程关联。给出了Hessian输运梯度流的几个示例以及相关的随机微分方程，包括反向Kullback-Leibler发散，\（\ alpha \）-发散，Hellinger距离，Pearson发散和Jenson-Shannon发散的示例。