标题： 关于通过梯度流采样时Kullback--Leibler散度的唯一性质的注记 显示英文标题

标题： A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flows

摘要： 我们考虑从概率分布$\pi$中进行采样的问题。众所周知，这可以写成一个在概率分布空间上的优化问题，在其中我们旨在最小化与$\pi$的差异。优化问题通常通过在概率分布空间中使用适当度量的梯度流来解决。我们证明，在Bregman差异族中，Kullback--Leibler差异是唯一一种其梯度流相对于许多流行的度量而言不需要知道$\pi$的归一化常数的差异。 显示英文摘要

摘要： We consider the problem of sampling from a probability distribution $\pi$. It is well known that this can be written as an optimisation problem over the space of probability distribution in which we aim to minimise a divergence from $\pi$. and The optimisation problem is normally solved through gradient flows in the space of probability distribution with an appropriate metric. We show that the Kullback--Leibler divergence is the only divergence in the family of Bregman divergences whose gradient flow w.r.t. many popular metrics does not require knowledge of the normalising constant of $\pi$.