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#wasserstein

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JMLR<p>'Wasserstein F-tests for Frechet regression on Bures-Wasserstein manifolds', by Haoshu Xu, Hongzhe Li.</p><p><a href="http://jmlr.org/papers/v26/24-0493.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">jmlr.org/papers/v26/24-0493.ht</span><span class="invisible">ml</span></a> <br> <br><a href="https://sigmoid.social/tags/wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>wasserstein</span></a> <a href="https://sigmoid.social/tags/covariates" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>covariates</span></a> <a href="https://sigmoid.social/tags/covariate" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>covariate</span></a></p>
JMLR<p>'Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models', by Xuefeng Gao, Hoang M. Nguyen, Lingjiong Zhu.</p><p><a href="http://jmlr.org/papers/v26/24-0902.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">jmlr.org/papers/v26/24-0902.ht</span><span class="invisible">ml</span></a> <br> <br><a href="https://sigmoid.social/tags/generative" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>generative</span></a> <a href="https://sigmoid.social/tags/wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>wasserstein</span></a> <a href="https://sigmoid.social/tags/models" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>models</span></a></p>
JMLR<p>'Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds', by Clément Bonet, Lucas Drumetz, Nicolas Courty.</p><p><a href="http://jmlr.org/papers/v26/24-0359.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">jmlr.org/papers/v26/24-0359.ht</span><span class="invisible">ml</span></a> <br> <br><a href="https://sigmoid.social/tags/manifolds" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>manifolds</span></a> <a href="https://sigmoid.social/tags/manifold" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>manifold</span></a> <a href="https://sigmoid.social/tags/wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>wasserstein</span></a></p>
JMLR<p>'Correction to "Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations"', by Daniel Paulin, Peter A. Whalley.</p><p><a href="http://jmlr.org/papers/v25/24-0895.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">jmlr.org/papers/v25/24-0895.ht</span><span class="invisible">ml</span></a> <br> <br><a href="https://sigmoid.social/tags/ergodic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ergodic</span></a> <a href="https://sigmoid.social/tags/wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>wasserstein</span></a> <a href="https://sigmoid.social/tags/approximations" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>approximations</span></a></p>
JMLR<p>'Entropic Gromov-Wasserstein Distances: Stability and Algorithms', by Gabriel Rioux, Ziv Goldfeld, Kengo Kato.</p><p><a href="http://jmlr.org/papers/v25/24-0039.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">jmlr.org/papers/v25/24-0039.ht</span><span class="invisible">ml</span></a> <br> <br><a href="https://sigmoid.social/tags/regularization" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>regularization</span></a> <a href="https://sigmoid.social/tags/wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>wasserstein</span></a> <a href="https://sigmoid.social/tags/variational" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>variational</span></a></p>
JMLR<p>'Wasserstein Proximal Coordinate Gradient Algorithms', by Rentian Yao, Xiaohui Chen, Yun Yang.</p><p><a href="http://jmlr.org/papers/v25/23-0889.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">jmlr.org/papers/v25/23-0889.ht</span><span class="invisible">ml</span></a> <br> <br><a href="https://sigmoid.social/tags/wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>wasserstein</span></a> <a href="https://sigmoid.social/tags/optimization" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>optimization</span></a> <a href="https://sigmoid.social/tags/gradient" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>gradient</span></a></p>
JMLR<p>'Characterization of translation invariant MMD on Rd and connections with Wasserstein distances', by Thibault Modeste, Clément Dombry.</p><p><a href="http://jmlr.org/papers/v25/22-1338.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">jmlr.org/papers/v25/22-1338.ht</span><span class="invisible">ml</span></a> <br> <br><a href="https://sigmoid.social/tags/wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>wasserstein</span></a> <a href="https://sigmoid.social/tags/measures" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>measures</span></a> <a href="https://sigmoid.social/tags/mmds" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mmds</span></a></p>
JMLR<p>'Adjusted Wasserstein Distributionally Robust Estimator in Statistical Learning', by Yiling Xie, Xiaoming Huo.</p><p><a href="http://jmlr.org/papers/v25/23-0379.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">jmlr.org/papers/v25/23-0379.ht</span><span class="invisible">ml</span></a> <br> <br><a href="https://sigmoid.social/tags/wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>wasserstein</span></a> <a href="https://sigmoid.social/tags/estimators" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>estimators</span></a> <a href="https://sigmoid.social/tags/robust" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>robust</span></a></p>
JMLR<p>'Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimization', by O. Deniz Akyildiz, Sotirios Sabanis.</p><p><a href="http://jmlr.org/papers/v25/21-1423.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">jmlr.org/papers/v25/21-1423.ht</span><span class="invisible">ml</span></a> <br> <br><a href="https://sigmoid.social/tags/wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>wasserstein</span></a> <a href="https://sigmoid.social/tags/nonasymptotic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>nonasymptotic</span></a> <a href="https://sigmoid.social/tags/stochastic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>stochastic</span></a></p>
JMLR<p>'Tangential Wasserstein Projections', by Florian Gunsilius, Meng Hsuan Hsieh, Myung Jin Lee.</p><p><a href="http://jmlr.org/papers/v25/23-0708.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">jmlr.org/papers/v25/23-0708.ht</span><span class="invisible">ml</span></a> <br> <br><a href="https://sigmoid.social/tags/wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>wasserstein</span></a> <a href="https://sigmoid.social/tags/projections" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>projections</span></a> <a href="https://sigmoid.social/tags/causal" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>causal</span></a></p>
JMLR<p>'Fair Data Representation for Machine Learning at the Pareto Frontier', by Shizhou Xu, Thomas Strohmer.</p><p><a href="http://jmlr.org/papers/v24/22-0005.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">jmlr.org/papers/v24/22-0005.ht</span><span class="invisible">ml</span></a> <br> <br><a href="https://sigmoid.social/tags/wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>wasserstein</span></a> <a href="https://sigmoid.social/tags/supervised" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>supervised</span></a> <a href="https://sigmoid.social/tags/fairness" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fairness</span></a></p>
JMLR<p>'A PDE approach for regret bounds under partial monitoring', by Erhan Bayraktar, Ibrahim Ekren, Xin Zhang.</p><p><a href="http://jmlr.org/papers/v24/22-1001.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">jmlr.org/papers/v24/22-1001.ht</span><span class="invisible">ml</span></a> <br> <br><a href="https://sigmoid.social/tags/wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>wasserstein</span></a> <a href="https://sigmoid.social/tags/forecaster" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>forecaster</span></a> <a href="https://sigmoid.social/tags/regret" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>regret</span></a></p>
Fabrizio Musacchio<p>Eliminating the middleman: You can apply the computation of the <a href="https://sigmoid.social/tags/Wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Wasserstein</span></a> distance even more directly in <a href="https://sigmoid.social/tags/WassersteinGANs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>WassersteinGANs</span></a> (<a href="https://sigmoid.social/tags/WGANs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>WGANs</span></a>), eliminating the need for a discriminator. </p><p>🌎 <a href="https://www.fabriziomusacchio.com/blog/2023-07-30-wgan_with_direct_wasserstein_distance/" rel="nofollow noopener" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">fabriziomusacchio.com/blog/202</span><span class="invisible">3-07-30-wgan_with_direct_wasserstein_distance/</span></a></p><p><a href="https://sigmoid.social/tags/MachineLearning" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MachineLearning</span></a></p>
Fabrizio Musacchio<p>The <a href="https://sigmoid.social/tags/Wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Wasserstein</span></a> <a href="https://sigmoid.social/tags/metric" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>metric</span></a> (<a href="https://sigmoid.social/tags/EMD" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>EMD</span></a>) can be used, to train <a href="https://sigmoid.social/tags/GenerativeAdversarialNetworks" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GenerativeAdversarialNetworks</span></a> (<a href="https://sigmoid.social/tags/GANs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GANs</span></a>) more effectively. This tutorial compares a default GAN with a <a href="https://sigmoid.social/tags/WassersteinGAN" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>WassersteinGAN</span></a> (<a href="https://sigmoid.social/tags/WGAN" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>WGAN</span></a>) trained on the <a href="https://sigmoid.social/tags/MNIST" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MNIST</span></a> dataset.</p><p>🌎 <a href="https://www.fabriziomusacchio.com/blog/2023-07-29-wgan/" rel="nofollow noopener" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">fabriziomusacchio.com/blog/202</span><span class="invisible">3-07-29-wgan/</span></a></p><p><a href="https://sigmoid.social/tags/MachineLearning" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MachineLearning</span></a></p>
Fabrizio Musacchio<p>Apart from <a href="https://sigmoid.social/tags/Wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Wasserstein</span></a> Distance (<a href="https://sigmoid.social/tags/EMD" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>EMD</span></a>), other <a href="https://sigmoid.social/tags/metrics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>metrics</span></a> also play an important role in <a href="https://sigmoid.social/tags/MachineLearning" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MachineLearning</span></a> tasks such as <a href="https://sigmoid.social/tags/clustering" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>clustering</span></a>, <a href="https://sigmoid.social/tags/classification" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>classification</span></a>, and <a href="https://sigmoid.social/tags/InformationRetrieval" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>InformationRetrieval</span></a>. In this tutorial, you can find a discussion of five commonly used metrics: EMD, <a href="https://sigmoid.social/tags/KullbackLeiblerDivergence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>KullbackLeiblerDivergence</span></a> (KL Divergence), <a href="https://sigmoid.social/tags/JensenShannonDivergence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JensenShannonDivergence</span></a> (JS Divergence), <a href="https://sigmoid.social/tags/TotalVariationDistance" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>TotalVariationDistance</span></a> (TV Distance), and <a href="https://sigmoid.social/tags/BhattacharyyaDistance" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>BhattacharyyaDistance</span></a>. </p><p>🌎 <a href="https://www.fabriziomusacchio.com/blog/2023-07-28-probability_density_metrics/" rel="nofollow noopener" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">fabriziomusacchio.com/blog/202</span><span class="invisible">3-07-28-probability_density_metrics/</span></a></p>
Fabrizio Musacchio<p>The <a href="https://sigmoid.social/tags/Wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Wasserstein</span></a> distance (<a href="https://sigmoid.social/tags/EMD" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>EMD</span></a>), sliced Wasserstein distance (<a href="https://sigmoid.social/tags/SWD" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SWD</span></a>), and the <a href="https://sigmoid.social/tags/L2norm" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>L2norm</span></a> are common <a href="https://sigmoid.social/tags/metrics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>metrics</span></a> used to quantify the ‘distance’ between two distributions. This tutorial compares these three metrics and discusses their advantages and disadvantages.</p><p>🌎 <a href="https://www.fabriziomusacchio.com/blog/2023-07-26-wasserstein_vs_l2_norm/" rel="nofollow noopener" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">fabriziomusacchio.com/blog/202</span><span class="invisible">3-07-26-wasserstein_vs_l2_norm/</span></a></p><p><a href="https://sigmoid.social/tags/OptimalTransport" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OptimalTransport</span></a> <a href="https://sigmoid.social/tags/MachineLearning" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MachineLearning</span></a></p>
Fabrizio Musacchio<p>This tutorial takes a different approach to explain the <a href="https://sigmoid.social/tags/Wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Wasserstein</span></a> distance (<a href="https://sigmoid.social/tags/EMD" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>EMD</span></a>) by approximating the <a href="https://sigmoid.social/tags/EMD" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>EMD</span></a> with cumulative distribution functions (<a href="https://sigmoid.social/tags/CDF" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>CDF</span></a>), providing a more intuitive understanding of the metric. </p><p>🌎 <a href="https://www.fabriziomusacchio.com/blog/2023-07-24-wasserstein_distance_cdf_approximation/" rel="nofollow noopener" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">fabriziomusacchio.com/blog/202</span><span class="invisible">3-07-24-wasserstein_distance_cdf_approximation/</span></a></p><p><a href="https://sigmoid.social/tags/OptimalTransport" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OptimalTransport</span></a></p>
Fabrizio Musacchio<p>Calculating the <a href="https://sigmoid.social/tags/Wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Wasserstein</span></a> distance (<a href="https://sigmoid.social/tags/EMD" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>EMD</span></a>) 📈 can be computational costly when using <a href="https://sigmoid.social/tags/LinearProgramming" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>LinearProgramming</span></a>. The <a href="https://sigmoid.social/tags/Sinkhorn" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Sinkhorn</span></a> algorithm provides a computationally efficient method for approximating the EMD, making it a practical choice for many applications, especially for large datasets 💫. Here is another tutorial, showing how to solve <a href="https://sigmoid.social/tags/OptimalTransport" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OptimalTransport</span></a> problem using the Sinkhorn algorithm in <a href="https://sigmoid.social/tags/Python" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Python</span></a> 🐍</p><p>🌎 <a href="https://www.fabriziomusacchio.com/blog/2023-07-23-wasserstein_distance_sinkhorn/" rel="nofollow noopener" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">fabriziomusacchio.com/blog/202</span><span class="invisible">3-07-23-wasserstein_distance_sinkhorn/</span></a></p>
Fabrizio Musacchio<p>The <a href="https://sigmoid.social/tags/Wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Wasserstein</span></a> distance 📐, aka Earth Mover’s Distance (<a href="https://sigmoid.social/tags/EMD" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>EMD</span></a>), provides a robust and insightful approach for comparing <a href="https://sigmoid.social/tags/ProbabilityDistributions" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ProbabilityDistributions</span></a> 📊. I’ve composed a <a href="https://sigmoid.social/tags/Python" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Python</span></a> tutorial 🐍 that explains the <a href="https://sigmoid.social/tags/OptimalTransport" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OptimalTransport</span></a> problem required to calculate EMD. It also shows how to solve the OT problem and calculate the EMD using the Python Optimal Transport (POT) library. Feel free to use and share it 🤗 </p><p>🌎 <a href="https://www.fabriziomusacchio.com/blog/2023-07-23-wasserstein_distance/" rel="nofollow noopener" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">fabriziomusacchio.com/blog/202</span><span class="invisible">3-07-23-wasserstein_distance/</span></a></p>
New Submissions to TMLR<p>Convergence of SGD for Training Neural Networks with Sliced Wasserstein Losses</p><p><a href="https://openreview.net/forum?id=aqqfB3p9ZA" rel="nofollow noopener" target="_blank"><span class="invisible">https://</span><span class="ellipsis">openreview.net/forum?id=aqqfB3</span><span class="invisible">p9ZA</span></a></p><p><a href="https://sigmoid.social/tags/sgd" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sgd</span></a> <a href="https://sigmoid.social/tags/wasserstein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>wasserstein</span></a> <a href="https://sigmoid.social/tags/generative" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>generative</span></a></p>
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