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arXiv Statistics ML By Yumiharu Nakano

Continuum-marginal optimal transport: a mesh-free kernel method

Read the original on arXiv Statistics ML →

The paper introduces a mesh‑free kernel method for continuum‑marginal optimal transport, aiming to recover the minimum‑energy velocity field that reproduces a continuous family of probability marginals. By embedding the weak continuity equation into a reproducing kernel Hilbert space, the authors obtain a sample‑only objective that eliminates spatial discretization. The velocity is represented via a linear‑in‑parameters dictionary or neural network and optimized with mini‑batch stochastic techniques, achieving accurate drift recovery and marginal consistency in synthetic experiments, and the framework also extends to the Nelson problem of stochastic optimal transport.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Statistics ML.

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