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Generalized Sliced Wasserstein Distances [article]

Soheil Kolouri, Kimia Nadjahi, Umut Simsekli, Roland Badeau, Gustavo K. Rohde
2019 arXiv   pre-print
We then utilize the generalized Radon transform to define a new family of distances for probability measures, which we call generalized sliced-Wasserstein (GSW) distances.  ...  The Wasserstein distance and its variations, e.g., the sliced-Wasserstein (SW) distance, have recently drawn attention from the machine learning community.  ...  Generalized Sliced-Wasserstein and Maximum Generalized Sliced-Wasserstein Distances Following the definition of the SW distance in Equation ( 7 ), we define the generalized sliced p-Wasserstein distance  ... 
arXiv:1902.00434v1 fatcat:tmcn2rsgtnfitnrlx57g4f46zy

Generative Modeling Using the Sliced Wasserstein Distance

Ishan Deshpande, Ziyu Zhang, Alexander Schwing
2018 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition  
distance rather than the Jenson-Shannon divergence.  ...  We found our approach to be significantly more stable compared to even the improved Wasserstein GAN.  ...  Conclusions In this paper we proposed to use the sliced Wasserstein distance for generative modeling.  ... 
doi:10.1109/cvpr.2018.00367 dblp:conf/cvpr/DeshpandeZS18 fatcat:2ewcg6v7mncmhotqykcih5jqbu

Generative Modeling using the Sliced Wasserstein Distance [article]

Ishan Deshpande, Ziyu Zhang, Alexander Schwing
2018 arXiv   pre-print
distance rather than the Jenson-Shannon divergence.  ...  We found our approach to be significantly more stable compared to even the improved Wasserstein GAN.  ...  Conclusions In this paper we proposed to use the sliced Wasserstein distance for generative modeling.  ... 
arXiv:1803.11188v1 fatcat:w24rmcq3wbbhpa5o23trx2z7ae

Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distance [article]

Kimia Nadjahi, Alain Durmus, Umut Şimşekli, Roland Badeau
2020 arXiv   pre-print
Emerging from computational optimal transport, the Sliced-Wasserstein (SW) distance has become a popular choice in MEDE thanks to its simplicity and computational benefits.  ...  Wasserstein generative adversarial networks, Wasserstein autoencoders).  ...  Sliced-Wasserstein distance.  ... 
arXiv:1906.04516v2 fatcat:f6ox4wmilncfveodwc5f72bdei

Max-Sliced Wasserstein Distance and its use for GANs [article]

Ishan Deshpande, Yuan-Ting Hu, Ruoyu Sun, Ayis Pyrros, Nasir Siddiqui, Sanmi Koyejo, Zhizhen Zhao, David Forsyth, Alexander Schwing
2019 arXiv   pre-print
We first show that the recently proposed sliced Wasserstein distance has compelling sample complexity properties when compared to the Wasserstein distance.  ...  To further improve the sliced Wasserstein distance we then analyze its 'projection complexity' and develop the max-sliced Wasserstein distance which enjoys compelling sample complexity while reducing projection  ...  Sample complexity of the Wasserstein and sliced Wasserstein distances We first show the benefits of using the sliced Wasserstein distance over the Wasserstein distance.  ... 
arXiv:1904.05877v1 fatcat:xvvod74kzbetjgygzgxgi4c6de

Max-Sliced Wasserstein Distance and Its Use for GANs

Ishan Deshpande, Yuan-Ting Hu, Ruoyu Sun, Ayis Pyrros, Nasir Siddiqui, Sanmi Koyejo, Zhizhen Zhao, David Forsyth, Alexander G. Schwing
2019 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
We first show that the recently proposed sliced Wasserstein distance has compelling sample complexity properties when compared to the Wasserstein distance.  ...  To further improve the sliced Wasserstein distance we then analyze its 'projection complexity' and develop the max-sliced Wasserstein distance which enjoys compelling sample complexity while reducing projection  ...  Sample complexity of the Wasserstein and sliced Wasserstein distances We first show the benefits of using the sliced Wasserstein distance over the Wasserstein distance.  ... 
doi:10.1109/cvpr.2019.01090 dblp:conf/cvpr/DeshpandeHSPSKZ19 fatcat:5pq3ivkskbacxej4zggbgitw4u

Point-set Distances for Learning Representations of 3D Point Clouds [article]

Trung Nguyen, Quang-Hieu Pham, Tam Le, Tung Pham, Nhat Ho, Binh-Son Hua
2021 arXiv   pre-print
From this study, we propose to use sliced Wasserstein distance and its variants for learning representations of 3D point clouds.  ...  We demonstrate the efficiency of the sliced Wasserstein metric and its variants on several tasks in 3D computer vision including training a point cloud autoencoder, generative modeling, transfer learning  ...  Generalized sliced Wasserstein distance First, we recall briefly the definition of generalized sliced Wasserstein distance [24] .  ... 
arXiv:2102.04014v2 fatcat:v25zyqkubjahdlbqp5mrd3pzt4

Orthogonal Estimation of Wasserstein Distances [article]

Mark Rowland and Jiri Hron and Yunhao Tang and Krzysztof Choromanski and Tamas Sarlos and Adrian Weller
2019 arXiv   pre-print
In this paper, we propose a new variant of sliced Wasserstein distance, study the use of orthogonal coupling in Monte Carlo estimation of Wasserstein distances and draw connections with stratified sampling  ...  Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations.  ...  The results for generative modelling are in Figure 6 (left for sliced Wasserstein distance, right for project Wasserstein distance). Red samples are those generated from the target distribution.  ... 
arXiv:1903.03784v2 fatcat:5va23hq3fffa5h6bjjzppfpwia

Distributional Sliced-Wasserstein and Applications to Generative Modeling [article]

Khai Nguyen and Nhat Ho and Tung Pham and Hung Bui
2020 arXiv   pre-print
Sliced-Wasserstein distance (SW) and its variant, Max Sliced-Wasserstein distance (Max-SW), have been used widely in the recent years due to their fast computation and scalability even when the probability  ...  Finally, we conduct extensive experiments with large-scale datasets to demonstrate the favorable performances of the proposed distances over the previous sliced-based distances in generative modeling applications  ...  Dual form of distributional generalized sliced-Wasserstein distance: Similar to the distributional sliced-Wasserstein distance, we use the dual form of distributional generalized sliced-Wasserstein distance  ... 
arXiv:2002.07367v2 fatcat:tlmpjroke5aifiqy34oqrfmxo4

Sliced Wasserstein Distance for Learning Gaussian Mixture Models

Soheil Kolouri, Gustavo K. Rohde, Heiko Hoffmann
2018 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition  
Wasserstein distance, which gives rise to a new algorithm.  ...  Specifically, we propose minimizing the sliced-Wasserstein distance between the mixture model and the data distribution with respect to the GMM parameters.  ...  GMMs and state the need for the sliced Wasserstein distance.  ... 
doi:10.1109/cvpr.2018.00361 dblp:conf/cvpr/KolouriRH18 fatcat:w7ftttndnzbtjk47gxbyvzfotu

Augmented Sliced Wasserstein Distances [article]

Xiongjie Chen, Yongxin Yang, Yunpeng Li
2022 arXiv   pre-print
In this work, we propose a new family of distance metrics, called augmented sliced Wasserstein distances (ASWDs), constructed by first mapping samples to higher-dimensional hypersurfaces parameterized  ...  The sliced Wasserstein distance and its variants improve the computational efficiency through the random projection, yet they suffer from low accuracy if the number of projections is not sufficiently large  ...  Sliced Wasserstein distance and generalized sliced Wasserstein distance: By applying the Radon transform to µ and ν to obtain multiple projections, the sliced Wasserstein distance (SWD) decomposes the  ... 
arXiv:2006.08812v7 fatcat:vzfdrmfnrvbyhlyeslqff6fzvm

Sliced Wasserstein Distance for Learning Gaussian Mixture Models [article]

Soheil Kolouri, Gustavo K. Rohde, Heiko Hoffmann
2017 arXiv   pre-print
Wasserstein distance, which gives rise to a new algorithm.  ...  Specifically, we propose minimizing the sliced-Wasserstein distance between the mixture model and the data distribution with respect to the GMM parameters.  ...  GMMs and state the need for the sliced Wasserstein distance.  ... 
arXiv:1711.05376v2 fatcat:rnl54ztwqjeo3fkkkx6znpgpby

Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model [article]

Soheil Kolouri, Phillip E. Pope, Charles E. Martin, Gustavo K. Rohde
2018 arXiv   pre-print
In this paper we study generative modeling via autoencoders while using the elegant geometric properties of the optimal transport (OT) problem and the Wasserstein distances.  ...  In short, we regularize the autoencoder loss with the sliced-Wasserstein distance between the distribution of the encoded training samples and a predefined samplable distribution.  ...  In this paper, we introduce a new type of autoencoders for generative modeling (Algorithm 1), which we call Sliced-Wasserstein Autoencoders (SWAE), that minimize the sliced-Wasserstein distance between  ... 
arXiv:1804.01947v3 fatcat:qzqvu76csjeidav45orf7uyq2q

Sliced Generative Models

Szymon Knop, Marcin Mazur, Jacek Tabor, Igor T. Podolak, Przemysław Spurek
2018 Schedae Informaticae  
In this paper we discuss a class of AutoEncoder based generative models based on one dimensional sliced approach.  ...  It turns out that both groups are correct generative models, but the second one gives a slightly faster decrease rate of Fréchet Inception Distance (FID).  ...  The obtained generative model was called the Sliced-Wasserstein AutoEncoder (SWAE).  ... 
doi:10.4467/20838476si.18.006.10411 fatcat:gli5ismcjbh5ngwtp6m2ax4lfq

Sliced Wasserstein Kernels for Probability Distributions

Soheil Kolouri, Yang Zou, Gustavo K. Rohde
2016 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
In this paper, we exploit the widely used kernel methods and provide a family of provably positive definite kernels based on the Sliced Wasserstein distance and demonstrate the benefits of these kernels  ...  Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as powerful discrepancy measures for probability distributions  ...  on a generic metric space.  ... 
doi:10.1109/cvpr.2016.568 dblp:conf/cvpr/KolouriZR16 fatcat:i3bfqfystzdwpfzovq2fn7syiu
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