The derivatives of Sinkhorn-Knopp converge
We show that the derivatives of the Sinkhorn-Knopp algorithm, or iterative proportional fitting procedure, converge towards the derivatives of the entropic regularization of the optimal transport problem with a locally uniform linear convergence rate.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A Sinkhorn-Newton method for entropic optimal transport
We consider the entropic regularization of discretized optimal transport and propose to solve its optimality conditions via a logarithmic Newton iteration. We show a quadratic convergence rate and validate numerically th…
Sinkhorn Algorithm for Sequentially Composed Optimal Transports
Sinkhorn algorithm is the de-facto standard approximation algorithm for optimal transport, which has been applied to a variety of applications, including image processing and natural language processing. In theory, the p…
Understanding Symmetric Smoothing Filters: A Gaussian Mixture Model Perspective
Many patch-based image denoising algorithms can be formulated as applying a smoothing filter to the noisy image. Expressed as matrices, the smoothing filters must be row normalized so that each row sums to unity. Surpris…
DenoisingImage DenoisingUnityEquivalence between the Fitness-Complexity and the Sinkhorn-Knopp algorithms
We uncover the connection between the Fitness-Complexity algorithm, developed in the economic complexity field, and the Sinkhorn-Knopp algorithm, widely used in diverse domains ranging from computer science and mathemati…
Phase transition of the Sinkhorn-Knopp algorithm
The matrix scaling problem, particularly the Sinkhorn-Knopp algorithm, has been studied for over 60 years. In practice, the algorithm often yields high-quality approximations within just a few iterations. Theoretically, …