Optimal Mass Transport: Signal processing and machine-learning applications

By Soheil Kolouri, Se Rim Park, Matthew Thorpe, Dejan Slepcev, Gustavo Kunde Rohde. 2017

477 citations recorded by the source corpus.

Transport-based techniques for signal and data analysis have recently received increased interest. Given their ability to provide accurate generative models for signal intensities and other data distributions, they have been used in a variety of applications, including content-based retrieval, cancer detection, image superresolution, and statistical machine learning, to name a few, and they have been shown to produce state-of-the-art results. Moreover, the geometric characteristics of transport-related metrics have inspired new kinds of algorithms for interpreting the meaning of data distributions. Here, we provide a practical overview of the mathematical underpinnings of mass transport-related methods, including numerical implementation, as well as a review, with demonstrations, of several applications. Software accompanying this article is available from [43].

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

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Citations in the corpus

Co-Transport for Class-Incremental Learning (2021, background): “With the ground cost, OT can find a coupling between two distributions, which can be viewed as the mapping between two sets [20, 41].”
SAR Image Classification Using Few-Shot Cross-Domain Transfer Learning (2019, background): “Optimal transport [33] is a suitable metric to deal with the above issues and due to be an effective metric, it has been used extensively in deep learning literature re-Algorithm Update entire parameters: end for cently [5, 4, 15, 28].”
Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning (2019, background): “rning with generative adversarial networks [2,41,45], domain adaptation [24,63], signal processing [106], etc. For a comprehensive survey of dierent applications of the optimal transport problem see [54,82]. The optimization problem in (5) constitutes an innite-dimensional linear program over the tr”
Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters (2018, background): “and finance [5], condensed matter physics [8], and other applications [26].”
Inferring spatial and signaling relationships between cells from single cell transcriptomic data (2020, unknown): “24 – 29).”
Generalized Sliced Wasserstein Distances (2019, background): “It has attracted abundant attention in data sciences and machine learning due to its convenient theoretical properties and applications on many domains [2, 3, 4, 5, 6, 7, 8], especially in implicit generative modeling such as OT-based generative adversarial networks (GANs) and variational auto-encod”
Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm (2018, background): “, 2017; Panaretos & Zemel, 2016), and other applications (Kolouri et al., 2017).”
Plugin estimation of smooth optimal transport maps (2021, background): “Optimal transport maps play a central role in the theory of optimal transport (Rachev and Rüschendorf, 1998; Villani, 2003; Santambrogio, 2015), and form an increasingly important methodology in statistics and machine learning (Kolouri et al., 2017; Panaretos and Zemel, 2019).”
Bayesian Learning with Wasserstein Barycenters (2018, background): “ding statistical applications, we refer to the recent survey [33] and the many references therein. In parallel, optimal transport has become increasingly popular within the machine learning community [28], though most of the published works have focused on the discrete setting (e.g., comparing histo”
Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits (2022, background): “Currently, this problem has several theoretical and practical applications in a variety of scientific fields, including statistics and machine learning [70], computer vision [71], linguistics [72], classical mechanics [73], and molecular biology [74].”
Sliced Wasserstein Distance for Learning Gaussian Mixture Models (2017, methodology): “Here, we propose, alternatively, to minimize the p-Wasserstein distance, and more specifically the sliced p-Wasserstein distance [27], between the data distribution and the GMM.”
Deep Transfer Learning for Few-Shot SAR Image Classification (2019, methodology): “For this reason, it has been found to be an effective metric and has been used extensively in the deep learning literature recently [16,23,29,30].”