A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices
1964/06/01 by Richard Sinkhorn · 1,038 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Applied mathematics #Mathematics #Matrix Theory and Algorithms #Pure mathematics #Statistics
paper · doi:10.1214/aoms/1177703591
published in The Annals of Mathematical Statistics 35(2), 876-879 (Institute of Mathematical Statistics)
openalex publication_date 1964/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Cited by
- Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation
- Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger Bridge
- anyakrakusuma: A Python Library for Entropic Schrödinger Bridges on Idealized Geometries
- Sharp Asymptotics for Regularized Optimal Transport
- Quantum Optimal Transport for Tensor Field Processing
- Stochastic Optimization for Large-scale Optimal Transport
- The Atlas for the Aspiring Network Scientist
- Residual Prior Diffusion: A Probabilistic Framework Integrating Coarse Latent Priors with Diffusion Models
- Dimension-Uniform Dynamics of Iterated Correlation Matrices
- Entropic selection for optimal transport on the line with distance cost
- Optimal Preconditioning is a Geodesically Convex Optimization Problem
- Tensor optimal transport, distance between sets of measures and tensor scaling
- TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics
- Informative Risk Measures in the Banking Industry: A Proposal based on the Magnitude-Propensity Approach
- Asymptotic relatively more efficient test with auxiliary information: the case of the Z-test and the chi-square test
- Multi-Text Guided Few-Shot Semantic Segmentation
- Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distribution to Multivariate Settings
- Unbiased Semantic Decoding with Vision Foundation Models for Few-shot Segmentation
- Stochastic Data Clustering
- An Efficient Algorithm for Minimizing Ordered Norms in Fractional Load Balancing
- Accelerated decomposition of bistochastic kernel matrices by low rank approximation
- Analysis of a Classical Matrix Preconditioning Algorithm
- From independent sets and vertex colorings to isotropic spaces and isotropic decompositions
- Relaxed Schroedinger bridges and robust network routing
- Semantics-Native Communication with Contextual Reasoning
- Cascading Feature Extraction for Fast Point Cloud Registration
- Fast Approximate Quadratic Programming for Large (Brain) Graph Matching
- Symmetrized Sinkhorn-Gibbs Inference for Oscillatory Inverse Problems
- Direct Measure Matching for Crowd Counting
- Kemeny's constant minimization for reversible Markov chains via structure-preserving perturbations
- Geometric Algorithms for Neural Combinatorial Optimization with Constraints
- ARCO-BO: Adaptive Resource-aware COllaborative Bayesian Optimization for Heterogeneous Multi-Agent Design
- A Differential Geometry Perspective on Orthogonal Recurrent Models
- Robust Point Cloud Registration Framework Based on Deep Graph Matching
- Stochastic control liaisons: Richard Sinkhorn meets Gaspard Monge on a Schroedinger bridge
- Aligning Multilingual News for Stock Return Prediction
- Sinkformers: Transformers with Doubly Stochastic Attention
- Accelerating the Sinkhorn-Knopp iteration by Arnoldi-type methods
- PermLLM: Learnable Channel Permutation for N:M Sparse Large Language Models
- SegMASt3R: Geometry Grounded Segment Matching
- Data-to-Energy Stochastic Dynamics
- Flow Matching with Semidiscrete Couplings
- LOTFormer: Doubly-Stochastic Linear Attention via Low-Rank Optimal Transport
- Unit Consistency, Generalized Inverses, and Effective System Design Methods
- Unsupervised Learning of Graph Hierarchical Abstractions with Differentiable Coarsening and Optimal Transport
- Graph-based Clustering Revisited: A Relaxation of Kernel k-Means Perspective
- An efficient algorithm for entropic optimal transport under martingale-type constraints
- Spectral convergence of diffusion maps: improved error bounds and an alternative normalisation
- GOT: An Optimal Transport framework for Graph comparison
- A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs
- Optimal Transport losses and Sinkhorn algorithm with general convex regularization
- Partial minimization of strict convex functions and tensor scaling
- Traversing the Schroedinger Bridge strait: Robert Fortet's marvelous proof redux
- Online Sinkhorn: Optimal Transport distances from sample streams
- From Alignment to Assignment: Frustratingly Simple Unsupervised Entity Alignment
- A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps
- Saddle Hierarchy in Dense Associative Memory
- Sparse Sinkhorn Attention
- PREDATOR: Registration of 3D Point Clouds with Low Overlap
- Low-Complexity Data-Parallel Earth Mover's Distance Approximations
- Identifying Network Hubs with the Partial Correlation Graphical LASSO
- Mapping in a cycle: Sinkhorn regularized unsupervised learning for point cloud shapes
- Dilation of stochastic matrices by coarse graining
- Point Cloud Registration using Representative Overlapping Points
- GEDAN: Learning the Edit Costs for Graph Edit Distance
- Wasserstein Distances on Quantum Structures: an Overview
- Scaling Algorithms for Unbalanced Transport Problems
- Zero-Shot Learning with Subsequence Reordering Pretraining for Compound-Protein Interaction
- On the notion of quantum copulas
- Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport
- Iterative Bregman Projections for Regularized Transportation Problems
- Loss of community identity in opinion dynamics models as a function of inter-group interaction strength
- Partitions of the polytope of Doubly Substochastic Matrices
- Robust Hadamard matrices, unistochastic rays in Birkhoff polytope and equi-entangled bases in composite spaces
- Matching Distributions via Optimal Transport for Semi-Supervised Learning
- Model Fusion via Optimal Transport
- Inference with Aggregate Data: An Optimal Transport Approach
- Sinkhorn AutoEncoders
- Phase transition of the Sinkhorn-Knopp algorithm
- Convergence rates for regularized unbalanced optimal transport: the discrete case
- Mask6D: Masked Pose Priors For 6D Object Pose Estimation
- The Monge optimal transport barycenter problem
- Structure-aware Semantic Discrepancy and Consistency for 3D Medical Image Self-supervised Learning
- Information Geometry Connecting Wasserstein Distance and Kullback-Leibler Divergence via the Entropy-Relaxed Transportation Problem
- Minimally dissipative multi-bit logical operations
- Importance sampling for weighted binary random matrices with specified margins
- Entropic Wasserstein Gradient Flows
- Counting magic squares in quasi-polynomial time
- Noise-tolerant tomography of multimode linear optical interferometers with single photons
- Schrödinger-Föllmer Sampler: Sampling without Ergodicity
- A Fast Projected Fixed-Point Algorithm for Large Graph Matching
- Annihilating and breaking Lorentz cone entanglement
- The empirical discrete copula process
- Kernel Density Balancing
- Learning Permutations with Sinkhorn Policy Gradient
- The LQR-Schrödinger Bridge
- Multi-marginal optimal transport and probabilistic graphical models
- Generalized Friedland-Tverberg inequality: applications and extensions
- On Fitting Flow Models with Large Sinkhorn Couplings
- Hierarchical Low-Rank Approximation of Regularized Wasserstein Distance
- Ranking via Sinkhorn Propagation
- Grasp2Grasp: Vision-Based Dexterous Grasp Translation via Schrödinger Bridges
- From Local Updates to Global Balance: A Framework for Distributed Matrix Scaling
- Closed Form of a Generalized Sinkhorn Limit
- Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and\n Costs
- PlueckerNet: Learn to Register 3D Line Reconstructions
- Optimal prediction of Markov chains with and without spectral gap
- Distributionally Robust Deep Q-Learning
- Stochastic Optimization for Regularized Wasserstein Estimators
- A Riemannian Optimization Approach for Finding the Nearest Reversible Markov Chain
- Iterative proportional scaling revisited: a modern optimization perspective
- Enumerating contingency tables via random permanents
- Barrier relaxations of the classical and quantum optimal transport problems
- The Wasserstein-Fisher-Rao metric for waveform based earthquake location
- AutoShuffleNet: Learning Permutation Matrices via an Exact Lipschitz Continuous Penalty in Deep Convolutional Neural Networks
- A Hölderian backtracking method for min-max and min-min problems
- Scaling of matrices to achieve specified row and column sums
- Asymptotic estimates for the number of contingency tables, integer flows, and volumes of transportation polytopes
- Minimizing relative entropy of path measures under marginal constraints
- Iterative Bregman Projections for Regularized Transportation Problems
- Improving Topic Modeling by Distilling Soft Labels from Language Models
- cuRegOT: A GPU-Accelerated Solver for Entropic-Regularized Optimal Transport
- Entropic continuity bounds for conditional covariances with applications to Schr" odinger and Sinkhorn bridges
- A Generalized Matrix Inverse That Is Consistent with Respect to Diagonal Transformations
- MESH: Memory-Efficient Sinkhorn Optimization for Mixture-of-Experts Training
- Learning Functions over Sets via Permutation Adversarial Networks
- Learning to Represent and Predict Sets with Deep Neural Networks
- Scalable Approximate Algorithms for Optimal Transport Linear Models
- Quantum Doubly Stochastic Transformers
- Toric invariant theory for maximum likelihood estimation in log-linear models
- Alternating Minimization, Scaling Algorithms, and the Null-Cone Problem from Invariant Theory
- A Bidirectional DeepParticle Method for Efficiently Solving Low-dimensional Transport Map Problems
- Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavity
- Deriving the Gradients of Some Popular Optimal Transport Algorithms
- Analyzing Transaction Graphs via Motif-Based Graph Representation Learning for Cryptocurrency Price Prediction
- Sinkhorn's theorem [wikipedia]
- ProDis-ContSHC: learning protein dissimilarity measures and hierarchical context coherently for protein-protein comparison in protein database retrieval. [europepmc]
- Fast approximate quadratic programming for graph matching. [europepmc]
- QuBiLS-MAS, open source multi-platform software for atom- and bond-based topological (2D) and chiral (2.5D) algebraic molecular descriptors computations. [europepmc]
- Feature Consistent Point Cloud Registration in Building Information Modeling. [europepmc]
- A Score-Based Approach for Training Schrödinger Bridges for Data Modelling. [europepmc]
- Wasserstein barycenter regression for estimating the joint dynamics of renewable and fossil fuel energy indices. [europepmc]
- Causal identification of single-cell experimental perturbation effects with CINEMA-OT. [europepmc]
- Conformal mirror descent with logarithmic divergences. [europepmc]
- A review of rigid point cloud registration based on deep learning. [europepmc]
- DiffPaSS-high-performance differentiable pairing of protein sequences using soft scores. [europepmc]
- Sinkhorn Distributionally Robust Conditional Quantile Prediction with Fixed Design. [europepmc]
- Image Matching: Foundations, State of the Art, and Future Directions. [europepmc]
- Modelling global trade with optimal transport. [europepmc]
- 3d-OT: a deep geometry-aware framework for heterogeneous slices alignment of spatial multi-omics. [europepmc]
- A Regularised Intent Model for Discovering Multiple Intents in E-Commerce Tail Queries [europepmc]