Figure 2 - available via license: Creative Commons Attribution 4.0 International
Content may be subject to copyright.
Contours of density functions of the entropy-regularized optimal coupling of N (0, 1) and N (5, 2) in three different parameters λ = 0.1, 1, 10. All of the optimal couplings are two-variate normal distributions.
Source publication
Distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions from other distances or divergences. Although computing the Wasserstein distance is costly, entropy-regularized optim...
Context in source publication
Similar publications
![Results for ε\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/356391107/figure/fig5/AS:1092083913883675@1637384503809/Results-for-edocumentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
We study Benamou’s domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove linear convergence of the algorithm with respect to the Kullback–Leibler divergence and illustrate the (poten...
![The Dynkin diagram of B2≃C2\documentclass[12pt]{minimal}...](publication/360481952/figure/fig1/AS:11431281091459730@1666491422027/The-Dynkin-diagram-of-B2C2documentclass12ptminimal-usepackageamsmath_Q320.jpg)
![The Dynkin diagram of G2\documentclass[12pt]{minimal}...](publication/360481952/figure/fig2/AS:11431281091489954@1666491422053/The-Dynkin-diagram-of-G2documentclass12ptminimal-usepackageamsmath_Q320.jpg)
We propose an effective framework for computing the prepotential of the topological B-model on a class of local Calabi–Yau geometries related to the circle compactification of five-dimensional N=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsf...
The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions from other distances or divergences. Although computing the Wasserstein distance is costly, entropy-regularized o...
![gα(x)\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/377749766/figure/fig2/AS:11431281220376202@1706410426933/gaxdocumentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
![A geometric interpretation of gα(x)\documentclass[12pt]{minimal}...](publication/377749766/figure/fig3/AS:11431281220367983@1706410427111/A-geometric-interpretation-of-gaxdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
![For β∈[0,∞)\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/377749766/figure/fig4/AS:11431281220367984@1706410427251/For-b0-documentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
The convexity of a set can be generalized to the two weaker notions of positive reach and r-convexity; both describe the regularity of a set’s boundary. For any compact subset of Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{...
We address the problem of minimizing a smooth function under smooth equality constraints. Under regularity assumptions on these constraints, we propose a notion of approximate first- and second-order critical point which relies on the geometric formalism of Riemannian optimization. Using a smooth exact penalty function known as Fletcher’s augmented...
