Sinkhorn算法的非等间距快速傅里叶变换Boost
Nonequispaced Fast Fourier Transform Boost for the Sinkhorn Algorithm
摘要：
这一贡献的特点是加速计算的辛克霍恩的算法，它近似的Wasserstein运输距离，采用非等间距快速傅里叶变换（NFFT）。所提出的算法允许近似的Wasserstein距离涉及不超过$\mathcal O(n\log n)$操作的概率测度支持的~ $n$点。此外，所提出的方法避免了昂贵的分配的特征矩阵。有了这个数值加速度，运输距离是可以达到的概率测度到目前为止。模拟和实际数据的数值试验证实了计算的优越性。
英文摘要：
This contribution features an accelerated computation of the Sinkhorn's algorithm, which approximates the Wasserstein transportation distance, by employing nonequispaced fast Fourier transforms (NFFT). The algorithm proposed allows approximations of the Wasserstein distance by involving not more than $\mathcal O(n\log n)$ operations for probability measures supported by~$n$ points. Furthermore, the proposed method avoids expensive allocations of the characterizing matrices. With this numerical acceleration, the transportation distance is accessible to probability measures out of reach so far. Numerical experiments using synthetic and real data affirm the computational advantage and superiority.
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