Unbalanced CO-Optimal Transport

• URL: http://arxiv.org/abs/2205.14923v2
• Date: Tue, 31 May 2022 13:17:54 GMT
• Title: Unbalanced CO-Optimal Transport
• Authors: Quang Huy Tran, Hicham Janati, Nicolas Courty, R\'emi Flamary, Ievgen Redko, Pinar Demetci, Ritambhara Singh
• Abstract summary: CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. We show that it is sensitive to outliers that are omnipresent in real-world data. This prompts us to propose unbalanced COOT for which we provably show its robustness to noise.
• Score: 16.9451175221198
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this approach leads to better alignments and generalizes both OT and Gromov-Wasserstein distances, we provide a theoretical result showing that it is sensitive to outliers that are omnipresent in real-world data. This prompts us to propose unbalanced COOT for which we provably show its robustness to noise in the compared datasets. To the best of our knowledge, this is the first such result for OT methods in incomparable spaces. With this result in hand, we provide empirical evidence of this robustness for the challenging tasks of heterogeneous domain adaptation with and without varying proportions of classes and simultaneous alignment of samples and features across single-cell measurements.

Related papers

• Propensity Score Alignment of Unpaired Multimodal Data [3.8373578956681555]
  Multimodal representation learning techniques typically rely on paired samples to learn common representations. This paper presents an approach to address the challenge of aligning unpaired samples across disparate modalities in multimodal representation learning.
  arXiv  Detail & Related papers  (2024-04-02T02:36:21Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Optimal Transport-Guided Conditional Score-Based Diffusion Models [63.14903268958398]
  Conditional score-based diffusion model (SBDM) is for conditional generation of target data with paired data as condition, and has achieved great success in image translation. To tackle the applications with partially paired or even unpaired dataset, we propose a novel Optimal Transport-guided Conditional Score-based diffusion model (OTCS) in this paper.
  arXiv  Detail & Related papers  (2023-11-02T13:28:44Z)
• Unbalanced Optimal Transport meets Sliced-Wasserstein [11.44982599214965]
  We propose two new loss functions based on the idea of slicing unbalanced OT, and study their induced topology and statistical properties. We show that the resulting methodology is modular as it encompasses and extends prior related work.
  arXiv  Detail & Related papers  (2023-06-12T15:15:00Z)
• Revisiting the Evaluation of Image Synthesis with GANs [55.72247435112475]
  This study presents an empirical investigation into the evaluation of synthesis performance, with generative adversarial networks (GANs) as a representative of generative models. In particular, we make in-depth analyses of various factors, including how to represent a data point in the representation space, how to calculate a fair distance using selected samples, and how many instances to use from each set.
  arXiv  Detail & Related papers  (2023-04-04T17:54:32Z)
• Learning Optimal Transport Between two Empirical Distributions with Normalizing Flows [12.91637880428221]
  We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. We show that a particular instance of invertible neural networks, namely the normalizing flows, can be used to approximate the solution of this OT problem.
  arXiv  Detail & Related papers  (2022-07-04T08:08:47Z)
• Unbalanced minibatch Optimal Transport; applications to Domain Adaptation [8.889304968879163]
  Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. We argue that the same minibatch strategy coupled with unbalanced optimal transport can yield more robust behavior. Our experimental study shows that in challenging problems associated to domain adaptation, the use of unbalanced optimal transport leads to significantly better results, competing with or surpassing recent baselines.
  arXiv  Detail & Related papers  (2021-03-05T11:15:47Z)
• Comparing Probability Distributions with Conditional Transport [63.11403041984197]
  We propose conditional transport (CT) as a new divergence and approximate it with the amortized CT (ACT) cost. ACT amortizes the computation of its conditional transport plans and comes with unbiased sample gradients that are straightforward to compute. On a wide variety of benchmark datasets generative modeling, substituting the default statistical distance of an existing generative adversarial network with ACT is shown to consistently improve the performance.
  arXiv  Detail & Related papers  (2020-12-28T05:14:22Z)
• Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptation [120.69747175899421]
  Optimal Transport (OT) distances such as Wasserstein have been used in several areas such as GANs and domain adaptation. We propose a computationally-efficient dual form of the robust OT optimization that is amenable to modern deep learning applications. Our approach can train state-of-the-art GAN models on noisy datasets corrupted with outlier distributions.
  arXiv  Detail & Related papers  (2020-10-12T17:13:40Z)
• Optimizing Vessel Trajectory Compression [71.42030830910227]
  In previous work we introduced a trajectory detection module that can provide summarized representations of vessel trajectories by consuming AIS positional messages online. This methodology can provide reliable trajectory synopses with little deviations from the original course by discarding at least 70% of the raw data as redundant. However, such trajectory compression is very sensitive to parametrization. We take into account the type of each vessel in order to provide a suitable configuration that can yield improved trajectory synopses.
  arXiv  Detail & Related papers  (2020-05-11T20:38:56Z)
• CO-Optimal Transport [19.267807479856575]
  Optimal transport (OT) is a powerful tool for finding correspondences and measuring similarity between two distributions. We propose a novel OT problem, named COOT for CO- Optimal Transport, that simultaneously optimize two transport maps between both samples and features. We demonstrate its versatility with two machine learning applications in heterogeneous domain adaptation and co-clustering/data summarization.
  arXiv  Detail & Related papers  (2020-02-10T13:33:15Z)

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.