DeepAI

# 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.

• 19 publications
• 20 publications
08/18/2021

### Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure

We establish the uniform in time stability, w.r.t. the marginals, of the...
10/18/2017

### A Sinkhorn-Newton method for entropic optimal transport

We consider the entropic regularization of discretized optimal transport...
06/24/2021

### Sharp Convergence Rates for Empirical Optimal Transport with Smooth Costs

We revisit the question of characterizing the convergence rate of plug-i...
12/08/2021

### Matching for causal effects via multimarginal optimal transport

Matching on covariates is a well-established framework for estimating ca...
06/28/2000

### Orthogonal Least Squares Algorithm for the Approximation of a Map and its Derivatives with a RBF Network

Radial Basis Function Networks (RBFNs) are used primarily to solve curve...
02/26/2023

### Root finding via local measurement

We consider the problem of numerically identifying roots of a target fun...
02/02/2020

### The Discrete Adjoint Method: Efficient Derivatives for Functions of Discrete Sequences

Gradient-based techniques are becoming increasingly critical in quantita...