Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transport

• URL: http://arxiv.org/abs/2410.03974v1
• Date: Fri, 4 Oct 2024 23:27:33 GMT
• Title: Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transport
• Authors: Milena Gazdieva, Jaemoo Choi, Alexander Kolesov, Jaewoong Choi, Petr Mokrov, Alexander Korotin,
• Abstract summary: We propose a novel, scalable approach for estimating the textitrobust continuous barycenter. Our method is framed as a $min$-$max$ optimization problem and is adaptable to textitgeneral cost function.
• Score: 84.51977664336056
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A common challenge in aggregating data from multiple sources can be formalized as an \textit{Optimal Transport} (OT) barycenter problem, which seeks to compute the average of probability distributions with respect to OT discrepancies. However, the presence of outliers and noise in the data measures can significantly hinder the performance of traditional statistical methods for estimating OT barycenters. To address this issue, we propose a novel, scalable approach for estimating the \textit{robust} continuous barycenter, leveraging the dual formulation of the \textit{(semi-)unbalanced} OT problem. To the best of our knowledge, this paper is the first attempt to develop an algorithm for robust barycenters under the continuous distribution setup. Our method is framed as a $\min$-$\max$ optimization problem and is adaptable to \textit{general} cost function. We rigorously establish the theoretical underpinnings of the proposed method and demonstrate its robustness to outliers and class imbalance through a number of illustrative experiments.

Related papers

• Estimating Barycenters of Distributions with Neural Optimal Transport [93.28746685008093]
  We propose a new scalable approach for solving the Wasserstein barycenter problem. Our methodology is based on the recent Neural OT solver. We also establish theoretical error bounds for our proposed approach.
  arXiv  Detail & Related papers  (2024-02-06T09:17:07Z)
• Energy-Guided Continuous Entropic Barycenter Estimation for General Costs [95.33926437521046]
  We propose a novel algorithm for approximating the continuous Entropic OT (EOT) barycenter for arbitrary OT cost functions. Our approach is built upon the dual reformulation of the EOT problem based on weak OT.
  arXiv  Detail & Related papers  (2023-10-02T11:24:36Z)
• Robust computation of optimal transport by $\beta$-potential regularization [79.24513412588745]
  Optimal transport (OT) has become a widely used tool in the machine learning field to measure the discrepancy between probability distributions. We propose regularizing OT with the beta-potential term associated with the so-called $beta$-divergence. We experimentally demonstrate that the transport matrix computed with our algorithm helps estimate a probability distribution robustly even in the presence of outliers.
  arXiv  Detail & Related papers  (2022-12-26T18:37:28Z)
• Variational Wasserstein Barycenters with c-Cyclical Monotonicity [17.26436842450489]
  We develop a novel continuous approximation method for the Wasserstein barycenters problem given sample access to the input distributions. We provide theoretical analysis on convergence and demonstrate the practical effectiveness of our method on real applications of posterior aggregation and synthetic data.
  arXiv  Detail & Related papers  (2021-10-22T11:06:50Z)
• Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimization [94.18714844247766]
  Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport. We present a scalable algorithm to compute Wasserstein-2 barycenters given sample access to the input measures.
  arXiv  Detail & Related papers  (2021-02-02T21:01:13Z)
• Continuous Regularized Wasserstein Barycenters [51.620781112674024]
  We introduce a new dual formulation for the regularized Wasserstein barycenter problem. We establish strong duality and use the corresponding primal-dual relationship to parametrize the barycenter implicitly using the dual potentials of regularized transport problems.
  arXiv  Detail & Related papers  (2020-08-28T08:28:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.