Wasserstein Iterative Networks for Barycenter Estimation

Korotin, Alexander; Egiazarian, Vage; Li, Lingxiao; Burnaev, Evgeny

doi:10.48550/arxiv.2201.12245

Cited by 3 publications

(7 citation statements)

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“…To address this issue, (Staib et al 2017;Claici, Chien, and Solomon 2018;Dvurechenskii et al 2018) assume the barycenter to be a finite set of points and rely on semi-discrete OT algorithms to compute the barycenter. The continuous approximation methods for Wasserstein barycenters remain unexplored until recently (Li et al 2020;Fan, Taghvaei, and Chen 2021;Korotin et al 2021bKorotin et al , 2022. Existing methods are based on dual potentials optimization or fixed point approaches.…”

Section: Introductionmentioning

confidence: 99%

“…Closely related to this paper are the recent works (Li et al 2020;Fan, Taghvaei, and Chen 2021;Korotin et al 2021b) that rely on the dual formulation of the Wasserstein barycenter and represent the dual potentials with neural networks. In particular, the method in (Li et al 2020) assumes a fixed prior as the proxy of the barycenter from the beginning, leading to inaccurate approximations especially for high-dimensional settings (Korotin et al 2022). For the specific ground cost, i.e., quadratic cost, (Fan, Taghvaei, and Chen 2021;Korotin et al 2021b) compute the barycenters under Wasserstein-2 distance.…”

Section: Introductionmentioning

confidence: 99%

“…However, the congruence regularization requires the selection of a prior distribution that is bounded below by the barycenter, which is a non-trivial task. On the other hand, (Korotin et al 2022) proposes an iterative algorithm for approximating the Wasserstein-2 barycenters based on the fixed point approach, where a generative network is used to parameterize the evolving barycenter. However, it is challenging to guarantee convergence to the true barycenter.…”

Section: Introductionmentioning

confidence: 99%

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Variational Wasserstein Barycenters with C-cyclical Monotonicity Regularization

Chi

Yang

et al. 2023

AAAI

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Wasserstein barycenter, built on the theory of Optimal Transport (OT), provides a powerful framework to aggregate probability distributions, and it has increasingly attracted great attention within the machine learning community. However, it is often intractable to precisely compute, especially for high dimensional and continuous settings. To alleviate this problem, we develop a novel regularization by using the fact that c-cyclical monotonicity is often necessary and sufficient conditions for optimality in OT problems, and incorporate it into the dual formulation of Wasserstein barycenters. For efficient computations, we adopt a variational distribution as the approximation of the true continuous barycenter, so as to frame the Wasserstein barycenters problem as an optimization problem with respect to variational parameters. Upon those ideas, we propose a novel end-to-end continuous approximation method, namely Variational Wasserstein Barycenters with c-Cyclical Monotonicity Regularization (VWB-CMR), given sample access to the input distributions. We show theoretical convergence analysis and demonstrate the superior performance of VWB-CMR on synthetic data and real applications of subset posterior aggregation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Variational Wasserstein Barycenters with C-cyclical Monotonicity Regularization

Chi

Yang

et al. 2023

AAAI

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“…To cope with this, fast methods aiming at learning and generating approximate Wasserstein barycenters on the basis of neural networks techniques, have also been proposed, see e.g. [31,32].…”

Section: Introductionmentioning

confidence: 99%

Bayesian learning with Wasserstein barycenters

Rios¹,

Backhoff-Veraguas²,

Fontbona³

et al. 2022

ESAIM: PS

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We introduce and study a novel model-selection strategy for Bayesian learning, based on optimal transport, along with its associated predictive posterior law: the Wasserstein population barycenter of the posterior law over models. We first show how this estimator, termed Bayesian Wasser- stein barycenter (BWB), arises naturally in a general, parameter-free Bayesian model-selection frame- work, when the considered Bayesian risk is the Wasserstein distance. Examples are given, illustrating how the BWB extends some classic parametric and non-parametric selection strategies. Furthermore, we also provide explicit conditions granting the existence and statistical consistency of the BWB, and discuss some of its general and specific properties, providing insights into its advantages compared to usual choices, such as the model average estimator. Finally, we illustrate how this estimator can be computed using the stochastic gradient descent (SGD) algorithm in Wasserstein space introduced in a companion paper [7], and provide a numerical example for experimental validation of the proposed method.

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“…, 𝜇 𝑁 are unknown with sample access, and develop stochastic optimization algorithms for approximating a Wasserstein barycenter with fixed support; see, e.g., [Claici, Chien, and Solomon, 2018, Staib, Claici, Solomon, and Jegelka, 2017, Krawtschenko, Uribe, Gasnikov, and Dvurechensky, 2020, Zhang, Qian, and Xie, 2023. Recently, numerical methods for continuous Wasserstein barycenter based on neural network parametrization or generative neural networks have been developed; see, e.g., [Cohen et al, 2020a, Fan, Taghvaei, and Chen, 2020, Korotin, Egiazarian, Li, and Burnaev, 2022, Korotin, Li, Solomon, and Burnaev, 2021, Li, Genevay, Yurochkin, and Solomon, 2020.…”

Section: Related Workmentioning

confidence: 99%

Numerical methods for model-free pricing in finance, optimal transport, and cyber risk management

Xiang

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Wasserstein Iterative Networks for Barycenter Estimation

Cited by 3 publications

References 0 publications

Variational Wasserstein Barycenters with C-cyclical Monotonicity Regularization

Variational Wasserstein Barycenters with C-cyclical Monotonicity Regularization

Bayesian learning with Wasserstein barycenters

Numerical methods for model-free pricing in finance, optimal transport, and cyber risk management

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