论文标题
重新审视流，缩放和熵：通过优化关节分布的统一视角
Flows, Scaling, and Entropy Revisited: a Unified Perspective via Optimizing Joint Distributions
论文作者
论文摘要
在此简短的说明中，我们描述了关于几种经典问题的统一算法观点，这些观点传统上在不同的社区中进行了研究。该透视图通过与关节概率分布P（x，y）相同的优化问题p（x，y）的相同镜头镜头镜头镜头镜头镜头p（x，y）的相同镜头镜头，这些视角 - 最佳传输，最小平均周期，矩阵缩放和矩阵平衡的问题。尽管这是通常引入最佳运输方式的方式，但对于其他三个问题，该镜头的传统明显较小。这种观点导致了一个简单而统一的框架，涵盖了问题制定，算法开发和运行时分析。
In this short expository note, we describe a unified algorithmic perspective on several classical problems which have traditionally been studied in different communities. This perspective views the main characters -- the problems of Optimal Transport, Minimum Mean Cycle, Matrix Scaling, and Matrix Balancing -- through the same lens of optimization problems over joint probability distributions P(x,y) with constrained marginals. While this is how Optimal Transport is typically introduced, this lens is markedly less conventional for the other three problems. This perspective leads to a simple and unified framework spanning problem formulation, algorithm development, and runtime analysis.
