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New method describes Wasserstein gradient flows for MMD functionals

By PulseAugur Editorial · [1 sources] ·

Researchers have developed a method to describe Wasserstein gradient flows for maximum mean discrepancy (MMD) functionals using a negative distance kernel. This approach characterizes these flows through solving an associated Cauchy problem on quantile functions, which are embeddings of the Wasserstein-2 space. The study provides a solution for this Cauchy problem, offering a piecewise linear formula for discrete target measures and demonstrating invariance and smoothing properties of the flow. AI

RANK_REASON The cluster contains an academic paper detailing a new mathematical method for analyzing gradient flows. [lever_c_demoted from research: ic=1 ai=0.4]

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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Richard Duong, Viktor Stein, Robert Beinert, Johannes Hertrich, Gabriele Steidl ·

    Wasserstein Gradient Flows of MMD Functionals with Distance Kernel and Cauchy Problems on Quantile Functions

    arXiv:2408.07498v5 Announce Type: replace-cross Abstract: We give a comprehensive description of Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals $\mathcal F_\nu := \text{MMD}_K^2(\cdot, \nu)$ towards given target measures $\nu$ on the real line, where we …

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