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Poster
Wasserstein Iterative Networks for Barycenter Estimation
Alexander Korotin · Vage Egiazarian · Lingxiao Li · Evgeny Burnaev

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Wasserstein barycenters have become popular due to their ability to represent the average of probability measures in a geometrically meaningful way. In this paper, we present an algorithm to approximate the Wasserstein-2 barycenters of continuous measures via a generative model. Previous approaches rely on regularization (entropic/quadratic) which introduces bias or on input convex neural networks which are not expressive enough for large-scale tasks. In contrast, our algorithm does not introduce bias and allows using arbitrary neural networks. In addition, based on the celebrity faces dataset, we construct Ave, celeba! dataset which can be used for quantitative evaluation of barycenter algorithms by using standard metrics of generative models such as FID.

Keywords: optimal transport · Neural Networks · Wasserstein-2 distance · continuous barycenter

Author Information

Alexander Korotin (Skolkovo Institute of Science and Technology)
Vage Egiazarian (Skoltech)
Lingxiao Li (MIT)
Evgeny Burnaev (Skoltech)

Evgeny Burnaev obtained his MSc in Applied Physics and Mathematics from the Moscow Institute of Physics and Technology in 2006. After successfully defending his PhD thesis in Foundations of Computer Science at the Institute for Information Transmission Problem RAS (IITP RAS) in 2008, Evgeny stayed with the Institute as a head of IITP Data Analysis and Predictive Modeling Lab. Since 2007 Evgeny Burnaev carried out a number of successful industrial projects with Airbus, SAFT, IHI, and Sahara Force India Formula 1 team among others. The corresponding data analysis algorithms, developed by Evgeny Burnaev and his scientific group, formed a core of the algorithmic software library for metamodeling and optimization. Thanks to the developed functionality, engineers can construct fast mathematical approximations to long running computer codes (realizing physical models) based on available data and perform design space exploration for trade-off studies. The software library passed the final Technology Readiness Level 6 certification in Airbus. According to Airbus experts, application of the library “provides the reduction of up to 10% of lead time and cost in several areas of the aircraft design process”. Nowadays a spin-off company Datadvance develops a Software platform for Design Space Exploration with GUI based on this algorithmic core. Since 2016 Evgeny Burnaev works as Associate Professor of Skoltech and manages his research group for Advanced Data Analytics in Science and Engineering For his scientific achievements in the year 2017 Evgeny Burnaev was honored with the Moscow Government Prize for Young Scientists in the category for the Transmission, Storage, Processing and Protection of Information for leading the project “The development of methods for predictive analytics for processing industrial, biomedical and financial data.”

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