Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks

Jiaojiao Fan, Amirhossein Taghvaei, Yongxin Chen
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:1571-1581, 2021.

Abstract

Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to approximate the Wasserstein Barycenters aiming at high-dimensional applications in machine learning. Our proposed algorithm is based on the Kantorovich dual formulation of the Wasserstein-2 distance as well as a recent neural network architecture, input convex neural network, that is known to parametrize convex functions. The distinguishing features of our method are: i) it only requires samples from the marginal distributions; ii) unlike the existing approaches, it represents the Barycenter with a generative model and can thus generate infinite samples from the barycenter without querying the marginal distributions; iii) it works similar to Generative Adversarial Model in one marginal case. We demonstratethe efficacy of our algorithm by comparing it with the state-of-art methods in multiple experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-fan21d, title = {Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks}, author = {Fan, Jiaojiao, Taghvaei, Amirhossein and Chen, Yongxin}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {1571--1581}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/fan21d/fan21d.pdf}, url = {https://proceedings.mlr.press/v139/fan21d.html}, abstract = {Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to approximate the Wasserstein Barycenters aiming at high-dimensional applications in machine learning. Our proposed algorithm is based on the Kantorovich dual formulation of the Wasserstein-2 distance as well as a recent neural network architecture, input convex neural network, that is known to parametrize convex functions. The distinguishing features of our method are: i) it only requires samples from the marginal distributions; ii) unlike the existing approaches, it represents the Barycenter with a generative model and can thus generate infinite samples from the barycenter without querying the marginal distributions; iii) it works similar to Generative Adversarial Model in one marginal case. We demonstratethe efficacy of our algorithm by comparing it with the state-of-art methods in multiple experiments.} }
Endnote
%0 Conference Paper %T Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks %A Jiaojiao Fan %A Amirhossein Taghvaei %A Yongxin Chen %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-fan21d %I PMLR %P 1571--1581 %U https://proceedings.mlr.press/v139/fan21d.html %V 139 %X Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to approximate the Wasserstein Barycenters aiming at high-dimensional applications in machine learning. Our proposed algorithm is based on the Kantorovich dual formulation of the Wasserstein-2 distance as well as a recent neural network architecture, input convex neural network, that is known to parametrize convex functions. The distinguishing features of our method are: i) it only requires samples from the marginal distributions; ii) unlike the existing approaches, it represents the Barycenter with a generative model and can thus generate infinite samples from the barycenter without querying the marginal distributions; iii) it works similar to Generative Adversarial Model in one marginal case. We demonstratethe efficacy of our algorithm by comparing it with the state-of-art methods in multiple experiments.
APA
Fan, J., Taghvaei, A. & Chen, Y.. (2021). Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:1571-1581 Available from https://proceedings.mlr.press/v139/fan21d.html.

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