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Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distance
[article]
2020
arXiv
pre-print
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Minimum expected distance estimation (MEDE) algorithms have been widely used for probabilistic models with intractable likelihood functions and they have become increasingly popular due to their use in ...
Emerging from computational optimal transport, the Sliced-Wasserstein (SW) distance has become a popular choice in MEDE thanks to its simplicity and computational benefits. ...
This work is partly supported by the French National Research Agency (ANR) as a part of the FBIMATRIX project (ANR-16-CE23-0014) and by the industrial chair Machine Learning for Big Data from Télécom ParisTech ...
arXiv:1906.04516v2
fatcat:f6ox4wmilncfveodwc5f72bdei
Approximate Bayesian Computation with the Sliced-Wasserstein Distance
[article]
2020
arXiv
pre-print
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Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood. ...
We propose a new ABC technique, called Sliced-Wasserstein ABC and based on the Sliced-Wasserstein distance, which has better computational and statistical properties. ...
However, each iteration requires n 2 operations, and there is no guarantee of convergence to Wp.
SLICED-WASSERSTEIN ABC Sliced-Wasserstein distance. ...
arXiv:1910.12815v2
fatcat:p7u6viu3lzgyjdho2rtk5lwtmm
Hilbert Sinkhorn Divergence for Optimal Transport
2021
2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
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It is therefore of theoretical demand to empower the Sinkhorn divergence with the capability of capturing nonlinear structures. ...
We also prove several attractive statistical properties of the proposed HSD, i.e., strong consistency, asymptotic behavior and sample complexity. ...
In other words, the sliced Wasserstein distance is calculated via linear slicing of the probability distribution. ...
doi:10.1109/cvpr46437.2021.00383
fatcat:445micqmkrcjzpsvgaiyloswni
Minimax Confidence Intervals for the Sliced Wasserstein Distance
[article]
2020
arXiv
pre-print
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Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable ...
Specifically, we construct confidence intervals for the Sliced Wasserstein distance which have finite-sample validity under no assumptions or under mild moment assumptions. ...
Acknowledgments Tudor Manole would like to thank Niccolò Dalmasso for conversations which inspired the likelihood-free inference application in Section 7. ...
arXiv:1909.07862v2
fatcat:dhe2ml366nerfodhwr32nv6kvi
Tessellated Wasserstein Auto-Encoders
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:2005.09923v1 fatcat:ixc37eaxrra3plzo2trskfutve
Non-adversarial generative models such as variational auto-encoder (VAE), Wasserstein auto-encoders with maximum mean discrepancy (WAE-MMD), sliced-Wasserstein auto-encoder (SWAE) are relatively easy to ...
train and have less mode collapse compared to Wasserstein auto-encoder with generative adversarial network (WAE-GAN). ...
The Wasserstein distance is a true distance and has a finer topology to guarantee convergence when minimize the distance. ...
arXiv:2005.09923v2
fatcat:cg3qnrznznfqbpbzopk4tzdcc4
Learning with minibatch Wasserstein : asymptotic and gradient properties
[article]
2021
arXiv
pre-print
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, but also with defects such as loss of distance property. ...
Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. ...
Acknowledgements Authors would like to thank Thibault Séjourné and Jean Feydy for fruitful discussions. ...
arXiv:1910.04091v4
fatcat:wqdqgos4kbh7xa32lf5sefws3u
Exploiting Chain Rule and Bayes' Theorem to Compare Probability Distributions
[article]
2021
arXiv
pre-print
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2021 pre-print arXiv:2012.14100v4 fatcat:3piij74w2zaadfigme47hkhkleOther Versions
On a wide variety of benchmark datasets for generative modeling, substituting the default statistical distance of an existing generative adversarial network with CT is shown to consistently improve the ...
When applied to train a generative model, CT is shown to strike a good balance between mode-covering and mode-seeking behaviors and strongly resist mode collapse. ...
CT with feature space cooperatively trained with discriminator loss. (d-f) Sliced Wasserstein distance and CT in the sliced space. ...
arXiv:2012.14100v5
fatcat:u3qhz4lok5dpnbhudcnjtgjcua
Statistical Analysis of Wasserstein Distributionally Robust Estimators
[article]
2021
arXiv
pre-print
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Equipped with this prescription, we present a central limit theorem for the DRO estimator and provide a recipe for constructing compatible confidence regions that are useful for uncertainty quantification ...
for optimally selecting the size of the adversary's budget. ...
[50] , tree-sliced Wasserstein distance [55] , etc. ...
arXiv:2108.02120v1
fatcat:dadtqnmvl5bk7phxmqba2aesbi
Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projections
[article]
2022
arXiv
pre-print
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2021 pre-print arXiv:2106.15427v1 fatcat:qrts66auanakpcygfxox56g2r4
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits ...
We validate our theoretical findings on synthetic datasets, and illustrate the proposed approximation on a generative modeling problem. ...
Acknowledgments This work is partly supported by the industrial chair "Data Science & Artificial Intelligence for Digitalized Industry & Services" from Télécom Paris. U.Ş.' ...
arXiv:2106.15427v2
fatcat:fdsbbghdbffh3dpfyb2s3lyvmu
OUP accepted manuscript
2019
Information and Inference A Journal of the IMA
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Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. ...
We study asymptotic properties of such minimum Wasserstein distance estimators, complementing results derived by Bassetti, Bodini and Regazzini in 2006. ...
Acknowledgements The bootstrap experiments were in part performed on the Odyssey cluster supported by the FAS Division of Science, Research Computing Group at Harvard University. Pierre E. ...
doi:10.1093/imaiai/iaz003
fatcat:s6umcdcc6rfzbjrrd2borgpdpm
Controlling Wasserstein distances by Kernel norms with application to Compressive Statistical Learning
[article]
2021
arXiv
pre-print
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Based on the relations between the MMD and the Wasserstein distance, we provide guarantees for compressive statistical learning by introducing and studying the concept of Wasserstein learnability of the ...
Our work is motivated by the compressive statistical learning (CSL) theory, a general framework for resource-efficient large scale learning in which the training data is summarized in a single vector ( ...
Asymptotic guarantees for generative modeling
based on the smooth wasserstein distance. In H. Larochelle, M. Ranzato, R. Hadsell, M. F. Bal-
can, and H. ...
arXiv:2112.00423v2
fatcat:hnlpmfoxjjhlln22623nn2nluq
Improving Relational Regularized Autoencoders with Spherical Sliced Fused Gromov Wasserstein
[article]
2020
arXiv
pre-print
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Relational regularized autoencoder (RAE) is a framework to learn the distribution of data by minimizing a reconstruction loss together with a relational regularization on the latent space. ...
That approach has a weakness since it treats every slicing direction similarly, meanwhile several directions are not useful for the discriminative task. ...
learning models [29] . ...
arXiv:2010.01787v1
fatcat:t3clf5oqhfe45p57vspskmbuli
Hypothesis Test and Confidence Analysis with Wasserstein Distance on General Dimension
[article]
2022
arXiv
pre-print
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We develop a general framework for statistical inference with the 1-Wasserstein distance. ...
To address this problem, in this study, we develop a novel non-asymptotic Gaussian approximation for the empirical 1-Wasserstein distance. ...
Owing to this advantage, the Wasserstein distance has been utilized extensively in machine learning and related fields, such as in generative models (Arjovsky et al., 2017) , supervised learning (Frogner ...
arXiv:1910.07773v3
fatcat:bsxkjpfej5cvlh6dxwdht7jxpy
On Projection Robust Optimal Transport: Sample Complexity and Model Misspecification
[article]
2021
arXiv
pre-print
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Optimal transport (OT) distances are increasingly used as loss functions for statistical inference, notably in the learning of generative models or supervised learning. ...
We provide an asymptotic guarantee of two types of minimum PRW estimators and formulate a central limit theorem for max-sliced Wasserstein estimator under model misspecification. ...
A generic Riemannian supergradient ascent algorithm for solving this problem is given by U t+1 ← Retr Ut (γ t+1 ξ t+1 ) for any ξ t+1 ∈ subdiff F (U t ), ...
arXiv:2006.12301v5
fatcat:kvuhrbldizdltfhd4kotkmkbqi
Complementary Learning for Overcoming Catastrophic Forgetting Using Experience Replay
[article]
2019
arXiv
pre-print
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2019 pre-print arXiv:1903.04566v1 fatcat:n5cnkbuu75eydjf7htjakaayy4
Inspired from complementary learning systems theory, we address this challenge by learning a generative model that couples the current task to the past learned tasks through a discriminative embedding ...
We learn an abstract level generative distribution in the embedding that allows the generation of data points to represent the experience. ...
Acknowledgment We thank James McClelland, Amarjot Singh, Charles Martin, Nicholas Ketz, and Jeffrey Krichmar for helpful feedback in the development and analysis of this work and conceptual discussions ...
arXiv:1903.04566v2
fatcat:ctffog6qgvgbvd5kipd3ddku7a
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