Schrödinger桥的插入式估计
Plug-in estimation of Schrödinger bridges
AI总结：
提出一种名为Sinkhorn bridge的Schrödinger桥插入式估计方法，无需迭代模拟扩散或训练神经网络，通过修改静态熵最优传输势函数估计漂移，收敛速率依赖目标测度本征维数。
摘要：
我们提出了一种估计两个概率分布之间Schrödinger桥的流程。与现有方法不同，我们的方法不需要迭代模拟前向和后向扩散，也不需要训练神经网络来拟合未知的漂移项。相反，我们证明了通过求解源样本与目标样本之间的静态熵最优传输问题所获得的势函数，可以被修改以生成一个自然的插入式估计器，用于定义两个测度之间桥的随时间变化的漂移项。在极小假设下，我们展示了被称为Sinkhorn桥的提议方案，可证明地以依赖于目标测度本征维数的收敛速率估计Schrödinger桥。我们的方法结合了采样、理论及统计熵最优传输领域的成果。
英文摘要：
We propose a procedure for estimating the Schrödinger bridge between two probability distributions. Unlike existing approaches, our method does not require iteratively simulating forward and backward diffusions or training neural networks to fit unknown drifts. Instead, we show that the potentials obtained from solving the static entropic optimal transport problem between the source and target samples can be modified to yield a natural plug-in estimator of the time-dependent drift that defines the bridge between two measures. Under minimal assumptions, we show that our proposal, which we call the \emph{Sinkhorn bridge}, provably estimates the Schrödinger bridge with a rate of convergence that depends on the intrinsic dimensionality of the target measure. Our approach combines results from the areas of sampling, and theoretical and statistical entropic optimal transport.
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