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Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey.

Abdelwahed Khamis, Russell Tsuchida, Mohamed Tarek

    IEEE Transactions on Pattern Analysis and Machine Intelligence
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    Summary
    This summary is machine-generated.

    Optimal Transport (OT) is a powerful mathematical framework increasingly used in machine learning. This survey focuses on scalable OT methods for big data challenges, offering a unified taxonomy and future research directions.

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    Area of Science:

    • Machine Learning
    • Optimization
    • Computational Mathematics

    Background:

    • Optimal Transport (OT) is a classical mathematical framework with a long history.
    • Recent years have seen significant contributions of OT to machine learning.
    • Addressing the computational demands of big and high-dimensional data is crucial for ML applications.

    Purpose of the Study:

    • To provide a comprehensive survey of Optimal Transport applications in machine learning.
    • To focus on the critical challenge of scalable Optimal Transport.
    • To present a unified taxonomy of existing scaling methods.

    Main Methods:

    • Systematic analysis of literature on scaling OT methods.
    • Categorization of scaling techniques into a unified taxonomy.
    • Explanation of OT background, formulations, properties, and applications.

    Main Results:

    • Identification of various OT formulations and their machine learning applications.
    • A structured overview of methods for scaling OT to handle large datasets.
    • A taxonomy classifying different approaches to scalable OT.

    Conclusions:

    • Optimal Transport offers powerful tools for machine learning, particularly for data analysis and comparison.
    • Scalability remains a key challenge, with ongoing research in developing efficient algorithms.
    • Future research directions include addressing open challenges in scalable OT and its broader ML integration.