论文标题
低量张量近似值用于解决多界限最佳运输问题
Low-rank tensor approximations for solving multi-marginal optimal transport problems
论文作者
论文摘要
通过添加熵正则化，可以将多 - 边界最佳运输问题转换为张量缩放问题，可以使用多核心sndhorn算法进行数值求解。该算法的主要计算瓶颈是对边际的重复评估。最近，有人建议当应用程序具有基础图形模型时，可以加速此评估。在这项工作中，我们通过将图形模型的张量网络二重要与其他低级近似值相结合，进一步加速了计算。我们提供了几个图像之间的颜色传递的示例，其中这些额外的低级别近似值节省了计算时间的96％以上。
By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of this algorithm is the repeated evaluation of marginals. Recently, it has been suggested that this evaluation can be accelerated when the application features an underlying graphical model. In this work, we accelerate the computation further by combining the tensor network dual of the graphical model with additional low-rank approximations. We provide an example for the color transfer between several images, in which these additional low-rank approximations save more than 96% of the computation time.
