Sinkhorn距离：最佳运输距离的光速计算
Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances
摘要：
最优运输距离是直方图参数化距离的基本族。尽管它们具有吸引人的理论特性，在检索任务和直观的配方中表现出色，但它们的计算涉及线性规划的分辨率，每当直方图的维数超过几百时，其成本是令人望而却步的。在这项工作中，我们提出了一个新的家庭的最佳运输距离，从最大熵的角度来看运输问题。我们平滑的经典最优运输问题的熵正则化项，并表明，由此产生的最佳也是一个距离，可以计算通过Sinkhorn-Knopp的矩阵缩放算法的速度是几个数量级的速度比运输求解。我们还报告了MNIST基准问题的经典最佳运输距离的性能提高。
英文摘要：
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation involves the resolution of a linear program whose cost is prohibitive whenever the histograms' dimension exceeds a few hundreds. We propose in this work a new family of optimal transportation distances that look at transportation problems from a maximum-entropy perspective. We smooth the classical optimal transportation problem with an entropic regularization term, and show that the resulting optimum is also a distance which can be computed through Sinkhorn-Knopp's matrix scaling algorithm at a speed that is several orders of magnitude faster than that of transportation solvers. We also report improved performance over classical optimal transportation distances on the MNIST benchmark problem.
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。
