Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey

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.