Related papers: Phase transition of the Sinkhorn-Knopp algorithm
A new method is presented which allows time averaged density matrices of closed quantum systems to be computed via a constraint overlap maximization. Due to its simplicity, this method can be combined with algorithms based on tensor…
A fundamental problem in shape matching and geometric similarity is computing the maximum area overlap between two polygons under translation. For general simple polygons, the best-known algorithm runs in $O((nm)^2 \log(nm))$ time [Mount,…
We study two fundamental optimization problems: (1) scaling a symmetric positive definite matrix by a positive diagonal matrix so that the resulting matrix has row and column sums equal to 1; and (2) minimizing a quadratic function subject…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
The Schr\"odinger bridge problem seeks the optimal stochastic process that connects two given probability distributions with minimal energy modification. While the Sinkhorn algorithm is widely used to solve the static optimal transport…
A recent breakthrough in Edmonds' problem showed that the noncommutative rank can be computed in deterministic polynomial time, and various algorithms for it were devised. However, only quite complicated algorithms are known for finding a…
Matrix denoising is central to signal processing and machine learning. Its statistical analysis when the matrix to infer has a factorised structure with a rank growing proportionally to its dimension remains a challenge, except when it is…
We consider time-dependent dynamical systems arising as sequential compositions of self-maps of a probability space. We establish conditions under which the Birkhoff sums for multivariate observations, given a centering and a general…
Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We…
Many applications, including rank aggregation and crowd-labeling, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and columns. We consider the problem of estimating such a matrix based on…
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…
We provide theoretical analyses for two algorithms that solve the regularized optimal transport (OT) problem between two discrete probability measures with at most $n$ atoms. We show that a greedy variant of the classical Sinkhorn…
We prove that the Sinkhorn algorithm converges at a rate of $O(k^{-1} \log k)$ in $\ell_1$-norm marginal error, in the asymptotically scalable case. This almost closes the gap between the lower bound $\Omega(k^{-1})$ (Qu et al., 2025) and…
Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…
Since the control of the Lipschitz constant has a great impact on the training stability, generalization, and robustness of neural networks, the estimation of this value is nowadays a real scientific challenge. In this paper we introduce a…
We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…
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 mathematics to economics.…
Osborne's iteration is a method for balancing $n\times n$ matrices which is widely used in linear algebra packages, as balancing preserves eigenvalues and stabilizes their numeral computation. The iteration can be implemented in any norm…
A key problem in process control is to decide which inputs should control which outputs. There are multiple ways to solve this problem, among them using gramian based measures, which include the Hankel interaction index array, the…
Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this…