Meta Optimal Transport

• URL: http://arxiv.org/abs/2206.05262v2
• Date: Fri, 2 Jun 2023 21:45:43 GMT
• Title: Meta Optimal Transport
• Authors: Brandon Amos, Samuel Cohen, Giulia Luise, Ievgen Redko
• Abstract summary: We study the use of amortized optimization to predict optimal transport maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and information present from past problems to rapidly predict and solve new problems.
• Score: 24.69258558871181
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and information present from past problems to rapidly predict and solve new problems. Otherwise, standard methods ignore the knowledge of the past solutions and suboptimally re-solve each problem from scratch. We instantiate Meta OT models in discrete and continuous settings between grayscale images, spherical data, classification labels, and color palettes and use them to improve the computational time of standard OT solvers. Our source code is available at http://github.com/facebookresearch/meta-ot

Related papers

• Semi-Discrete Optimal Transport: Nearly Minimax Estimation With Stochastic Gradient Descent and Adaptive Entropic Regularization [38.67914746910537]
  We prove an $mathcalO(t-1)$ lower bound rate for the OT map, using the similarity between Laguerre cells estimation and density support estimation. To nearly achieve the desired fast rate, we design an entropic regularization scheme decreasing with the number of samples.
  arXiv  Detail & Related papers  (2024-05-23T11:46:03Z)
• 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)
• Anchor Space Optimal Transport: Accelerating Batch Processing of Multiple OT Problems [13.846014191157405]
  We propose a translated OT problem designated as the anchor space optimal transport (ASOT) problem. For the proposed ASOT problem, the distributions will be mapped into a shared anchor point space, which learns the potential common characteristics. Based on the proposed ASOT, the Wasserstein distance error to the original OT problem is proven to be bounded by ground cost errors.
  arXiv  Detail & Related papers  (2023-10-24T18:55:12Z)
• Learning representations that are closed-form Monge mapping optimal with application to domain adaptation [24.258758784011572]
  Optimal transport (OT) is a powerful tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden. We propose to tackle these challenges using representation learning.
  arXiv  Detail & Related papers  (2023-05-12T14:14:39Z)
• STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization [74.1615979057429]
  We investigate non-batch optimization problems where the objective is an expectation over smooth loss functions. Our work builds on the STORM algorithm, in conjunction with a novel approach to adaptively set the learning rate and momentum parameters.
  arXiv  Detail & Related papers  (2021-11-01T15:43:36Z)
• Memory-Based Optimization Methods for Model-Agnostic Meta-Learning and Personalized Federated Learning [56.17603785248675]
  Model-agnostic meta-learning (MAML) has become a popular research area. Existing MAML algorithms rely on the episode' idea by sampling a few tasks and data points to update the meta-model at each iteration. This paper proposes memory-based algorithms for MAML that converge with vanishing error.
  arXiv  Detail & Related papers  (2021-06-09T08:47:58Z)
• A Survey on Optimal Transport for Machine Learning: Theory and Applications [1.1279808969568252]
  Optimal Transport (OT) theory has seen an increasing amount of attention from the computer science community. We present a brief introduction and history, a survey of previous work and propose directions of future study.
  arXiv  Detail & Related papers  (2021-06-03T16:10:42Z)
• Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark [133.46066694893318]
  We evaluate the performance of neural network-based solvers for optimal transport. We find that existing solvers do not recover optimal transport maps even though they perform well in downstream tasks.
  arXiv  Detail & Related papers  (2021-06-03T15:59:28Z)
• Manifold optimization for optimal transport [34.88495814664577]
  Optimal transport (OT) has recently found widespread interest in machine learning. We discuss how to approach OT problems within the framework of the manifold optimization. We make available the Manifold optimization-based Optimal Transport, or MOT, repository with codes useful in solving OT problems in Python and Matlab.
  arXiv  Detail & Related papers  (2021-03-01T10:49:19Z)
• Semi-Supervised Learning with Meta-Gradient [123.26748223837802]
  We propose a simple yet effective meta-learning algorithm in semi-supervised learning. We find that the proposed algorithm performs favorably against state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-07-08T08:48:56Z)
• Tracking Road Users using Constraint Programming [79.32806233778511]
  We present a constraint programming (CP) approach for the data association phase found in the tracking-by-detection paradigm of the multiple object tracking (MOT) problem. Our proposed method was tested on a motorized vehicles tracking dataset and produces results that outperform the top methods of the UA-DETRAC benchmark.
  arXiv  Detail & Related papers  (2020-03-10T00:04:32Z)

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.