The Sinkhorn-Knopp derivatives converge with linear rate.
problem Optimal transport problem with entropic regularization.
method Iterative proportional fitting procedure.
result Derivatives converge with linear rate.
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48 results for “sinkhorn regularization”
We introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures. After identifying neglectable components of the dual solution of the regularized Sinkhorn problem, we propose to screen those components by directly setting them at that value before entering t…
Optimal transport with -divergence regularization using generalized Sinkhorn algorithm.
problem Optimal transport with -divergence regularization.
method Generalized Sinkhorn algorithm for solving optimal transport problems with various -divergences.
result Strong duality holds, optimums are attained, and convergence to an optimal solution is guaranteed under certain conditions.
A new method for faster estimation of Wasserstein distance using Sinkhorn divergence.
problem Estimating the squared Wasserstein distance between probability distributions.
method Proposes a new estimator based on the Sinkhorn divergence with debiasing terms, and analyzes its sample complexity and computational efficiency.
result The proposed estimator allows higher regularization levels, leading to improved computational complexity and speedup in practice.
New initialization methods speed up Sinkhorn algorithm for OT problems.
problem Improving runtime of the Sinkhorn algorithm for optimal transport problems.
method Data-dependent initializers for Sinkhorn algorithm, based on closed-form solutions for specific settings.
result Data-dependent initializers result in dramatic speed-ups without affecting differentiability.
Paper proposes SinkhornDRL for distributional RL using Sinkhorn divergence and regularized Wasserstein loss.
problem Improving distributional reinforcement learning by minimizing Bellman return distribution differences.
method Introduces SinkhornDRL, a distributional RL algorithm using Sinkhorn divergence and regularized Wasserstein loss.
result SinkhornDRL consistently outperforms or matches existing algorithms on Atari games, especially in multi-dimensional reward settings.
We provide a computational complexity analysis for the Sinkhorn algorithm that solves the entropic regularized Unbalanced Optimal Transport (UOT) problem between two measures of possibly different masses with at most components. We show that the complexity of the Sinkhorn algorithm for finding an -appr…
SinSim improves self-supervised learning by integrating optimal transport into contrastive learning.
problem Lack of explicit regularization in contrastive learning methods leads to suboptimal generalization.
method Integrates Sinkhorn regularization from optimal transport theory into SimCLR.
result SinSim outperforms SimCLR and other self-supervised methods on various datasets.
Computational Guarantees for Doubly Entropic Wasserstein Barycenters via Damped Sinkhorn Iterationsmath.OC
New algorithm for computing Wasserstein barycenters with guarantees.
problem Computing Wasserstein barycenters with varying regularization strengths.
method Damped Sinkhorn iterations followed by exact maximization/minimization steps.
result First non-asymptotic convergence guarantees for approximating Wasserstein barycenters.
Debiased Wasserstein barycenters improve on entropy regularization in OT.
problem Entropy regularization in OT introduces bias, leading to blurred barycenters.
method Propose debiased Wasserstein barycenters using Sinkhorn iterations.
result Debiased barycenters preserve fast Sinkhorn-like iterations without entropy smoothing bias.
Study convergence and approximations of entropic regularized Wasserstein distances for Gaussian and RKHS measures.
problem Convergence and approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settings.
method Analysis of convergence and finite sample approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settings.
result Strictly weaker convergence in 2-Sinkhorn divergence for Gaussian measures compared to exact 2-Wasserstein distance.
Optimizes distributions robustly with Sinkhorn distance.
problem Distributionally robust optimization with Wasserstein distance.
method Convex programming dual reformulation, stochastic mirror descent algorithm.
result Demonstrates superior performance in synthetic and real data.
Sinkhorn Flow: A Continuous-Time Framework for Understanding and Generalizing the Sinkhorn Algorithmcs.LG
Continuous-time Sinkhorn flow generalizes and unifies existing dynamics.
problem Entropy-regularized optimal transport problems.
method Continuous-time mirror descent framework.
result Unified perspective on various dynamics in ML and math.
A new method reduces the computational cost of Sinkhorn algorithm for OT and UOT problems.
problem High computational complexity of Sinkhorn algorithm for OT and UOT problems.
method Importance sparsification method called Spar-Sink to efficiently approximate entropy-regularized OT and UOT solutions.
result The method reduces computational cost from to , and is consistent under mild regularity conditions.
Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by a regularized version that is less accurate but easy to differentiate. In this …
The Sinkhorn "distance", a variant of the Wasserstein distance with entropic regularization, is an increasingly popular tool in machine learning and statistical inference. However, the time and memory requirements of standard algorithms for computing this distance grow quadratically with the size of the data, making th…
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 that the method compares favorably with the more commonly used Sinkhorn--Knopp algorithm for small reg…
We present several new complexity results for the entropic regularized algorithms that approximately solve the optimal transport (OT) problem between two discrete probability measures with at most atoms. First, we improve the complexity bound of a greedy variant of Sinkhorn, known as \textit{Greenkhorn}, from $\wid…
This work studies Gaussian geometry under entropy-regularized 2-Wasserstein distance.
problem Understanding Gaussian distributions in uncertainty quantification and diffusivity.
method Entropy-regularized 2-Wasserstein distance, closed-form solutions, fixed-point characterization.
result Closed-form expressions for the 2-Sinkhorn divergence and fixed-point barycenter.
New stability theory for Sinkhorn semigroups with explicit decay rates.
problem Stability and convergence of Sinkhorn iterations for various divergences.
method Operator-theoretic framework based on Lyapunov techniques.
result Explicit exponential decay rates for Sinkhorn iterates.
SNS accelerates Sinkhorn algorithm with sparse Newton iterations.
problem Slow runtime of Sinkhorn algorithm for optimal transport.
method Early stopping and Newton-type subroutine for matrix scaling steps.
result SNS converges orders of magnitude faster than Sinkhorn.
The Sinkhorn flow converges to a Wasserstein mirror gradient flow from the Sinkhorn algorithm.
problem Optimizing joint distributions using the Sinkhorn algorithm.
method Wasserstein mirror gradient flow derived from the Sinkhorn algorithm.
result The Sinkhorn flow converges to a Wasserstein mirror gradient flow.
This paper refines the Gaussian Sinkhorn algorithm for general multivariate models.
problem Finite-dimensional solutions for general Gaussian multivariate models.
method Recursive formulation of the Sinkhorn algorithm for Gaussian models, including closed form expressions of entropic transport maps and Schrödinger bridges.
result Refined convergence analysis of Gaussian Sinkhorn algorithms.
This paper tackles Sinkhorn DRO by reformulating it as a bilevel program and proposes sampling-based algorithms.
problem Distributionally robust optimization with ambiguity sets defined via the Sinkhorn discrepancy.
method Primal perspective reformulation as a bilevel program, double-loop and single-loop sampling-based algorithms.
result Simultaneously obtain the optimal robust decision and the worst-case distribution.
Optimal Transport (OT) distances are now routinely used as loss functions in ML tasks. Yet, computing OT distances between arbitrary (i.e. not necessarily discrete) probability distributions remains an open problem. This paper introduces a new online estimator of entropy-regularized OT distances between two such arbitr…
New stability bounds for Sinkhorn's algorithm in entropic optimal transport.
problem Stability and convergence of Sinkhorn's algorithm for entropic optimal transport.
method Semiconcavity approach to analyze stability and convergence.
result Exponential convergence of Sinkhorn's algorithm under semiconcavity conditions.
CO2 algorithm creates coresets for generic smooth divergences efficiently.
problem Efficiently creating coresets for generic smooth divergences.
method CO2 algorithm using functional Taylor expansion and maximum mean discrepancy minimization.
result Poly-logarithmically many data points suffice for Sinkhorn divergence approximation.
Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavitymath.PR
The paper analyzes stability and convergence rates of entropic and Sinkhorn potentials.
problem Stability and convergence rates of entropic and Sinkhorn potentials.
method Semiconcavity properties of entropic potentials and Schrödinger bridges.
result Exponential convergence rates for gradient and Hessian of Sinkhorn iterates.
Paper tackles robust model training with a new stochastic algorithm.
problem Training robust models against data distribution shift.
method Derives a novel dual formulation and proposes a nested stochastic gradient descent algorithm.
result Establishes polynomial iteration and sample complexities for large-scale DRO problems.
Large Sinkhorn couplings improve flow models in data generation tasks.
problem Training flow models with optimal transport couplings.
method Using large batches of source and target points, and applying entropic regularization with a low .
result Flow models perform better with large Sinkhorn couplings and low regularization.
WAVE improves stability in reinforcement learning by adaptively weighting critic's loss.
problem Inherent instability in actor-critic reinforcement learning algorithms.
method Wasserstein adaptive value estimation with Sinkhorn approximation.
result Achieves $\mathcal{O}\left(\frac{1}{k}
ight)$ convergence rate for critic's mean squared error.
Accelerates optimal transport computation by 10x with spectral insights.
problem Exponential slow-down of convergence in Entropic Optimal Transport as regularization weakens.
method Spectral insights and spectral warm-start strategy to mitigate convergence issues.
result Faster convergence compared to the reference method Sinkhorn algorithm.
New algorithm tackles low-rank constraints in optimal transport problems.
problem Optimal transport problems with low-rank constraints.
method Explicit factorization of low-rank couplings as a product of sub-coupling factors linked by a common marginal.
result Stationary convergence of the algorithm proved.
New framework for robust hypothesis testing using Sinkhorn uncertainty sets.
problem Non-convex robust hypothesis testing problem.
method Exact mixed-integer exponential conic reformulation and convex approximation.
result Satisfactory testing performance and computational efficiency.
Brenier approach for optimal transportation between a quasi-discrete measure and a discrete measurecs.CV
Correctly estimating the discrepancy between two data distributions has always been an important task in Machine Learning. Recently, Cuturi proposed the Sinkhorn distance which makes use of an approximate Optimal Transport cost between two distributions as a distance to describe distribution discrepancy. Although it ha…
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been studied in depth: unbalanced transport, which is robust to the presence of outli…
Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or regularized variations such as Sinkhorn distance. However, as we will demonstrate, regu…
The Sinkhorn flow is a gradient flow in a nonlocal Wasserstein geometry.
problem Entropy-regularized optimal transport and its applications.
method Thermodynamic interpretation of the Sinkhorn algorithm.
result The Sinkhorn flow is the gradient flow of entropy in a nonlocal Wasserstein geometry.
A new method speeds up computation of Sinkhorn divergences to linear time.
problem Expensive computation of Sinkhorn divergences for comparing probability distributions.
method Using positive features to approximate ground costs, reducing computation time to linear.
result Sinkhorn divergences can be computed in linear time, scaling as O(nr).
This study approximates distances between Gaussian processes and covariance operators using RKHS.
problem Approximating distances between Gaussian processes and covariance operators from finite samples.
method Using reproducing kernel Hilbert space (RKHS) covariance and cross-covariance operators, the study shows how to consistently and efficiently estimate Sinkhorn divergence from finite samples.
result Convergence rates are dimension-independent and of the same order as Hilbert-Schmidt distance.
Sliced-regularized OT improves transport plan accuracy.
problem Optimal transport (OT) approximation accuracy.
method Sliced-regularized optimal transport (SROT) formulation.
result SROT yields more accurate approximations of exact OT than entropic OT.
A new model corrects inhomogeneity in Optimal Transport with Boundary.
problem Inhomogeneity in UROT models for Optimal Transport with Boundary.
method Proposed a modified entropic regularization term to make UROT models homogeneous.
result Homogeneous UROT model preserves properties of standard UROT while correcting inhomogeneity.
cuRegOT accelerates GPU-based entropic OT solving.
problem Slow convergence and high computational cost of optimal transport on GPUs.
method High-performance GPU solver with algorithmic and architectural optimizations.
result Significant speedups over state-of-the-art solvers.
Study entropic regularization of Gaussian measures and processes on Hilbert space.
problem Regularizing 2-Wasserstein distance for infinite-dimensional Gaussian measures and processes.
method Minimum Mutual Information property, closed form formulas, Fréchet differentiability, Sinkhorn barycenter equation.
result Entropic 2-Wasserstein distance and Sinkhorn divergence are Fréchet differentiable in Hilbert space.
The paper studies how different entropic regularizations affect GAN solutions.
problem Improving numerical convergence and sparsity in GAN solutions.
method Entropic regularization of Wasserstein distance and Sinkhorn divergence.
result Entropy regularization promotes sparsity, while Sinkhorn divergence recovers unregularized solution.
New scalable algorithm for non-negative linear regression with entropy-regularized OT loss.
problem Generalizing task-specific linear models to broader applications.
method Sinkhorn-like scaling iterations for convex penalty and datafit terms.
result Simple multiplicative updates for various penalty and datafit terms.
In this report, we review the calculation of entropy-regularised Wasserstein loss introduced by Cuturi and document a practical implementation in PyTorch. Code is available at https://github.com/t-vi/pytorch-tvmisc/blob/master/wasserstein-distance/Pytorch_Wasserstein.ipynb
Improved online Sinkhorn algorithm for large-scale data processing.
problem Efficiency of Sinkhorn algorithm for large-scale data streams.
method Revisit and improve convergence analysis of online Sinkhorn algorithm, introduce compressed online Sinkhorn algorithm.
result New faster convergence rate for online Sinkhorn algorithm under certain conditions.