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Explore an in-depth conference talk where Marco Cuturi from Apple, France delivers a comprehensive overview of optimal transport (OT) computations, focusing specifically on the challenges of computing OT maps using samples from high-dimensional probability measures. The presentation begins with a review of popular methods for this computational task, including approaches that leverage neural architectures, before introducing innovative work on parameterizing OT problems with elastic costs. These elastic costs combine traditional squared Euclidean distance with regularizers such as the L1 norm. Learn about the unique properties of OT maps that follow such costs, and discover new methodologies for both computing ground truth OT maps with elastic costs and adaptively learning regularizer parameters. This 52-minute presentation was delivered at the 2024 SIAM Conference on Mathematics of Data Science, offering valuable insights for those interested in optimization, transportation problems, probability, neural networks, data science, and applied mathematics.
