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Kalman-Wasserstein Gradient Flows

[Moved Online] Hot Topics: Optimal transport and applications to machine learning and statistics May 04, 2020 - May 08, 2020

May 05, 2020 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Franca Hoffman (California Institute of Technology)
Location: MSRI: Online/Virtual
  • Ensemble Kalman Inversion

  • Kalman-Wasserstein metric

  • Gradient Flow

  • Mean-Field Fokker-Planck equation

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Kalman-Wasserstein Gradient Flows


We study a class of interacting particle systems that may be used for optimization. By considering the mean-field limit one obtains a nonlinear Fokker-Planck equation. This equation exhibits a gradient structure in probability space, based on a modified Wasserstein distance which reflects particle correlations: the Kalman-Wasserstein metric. This setting gives rise to a methodology for calibrating and quantifying uncertainty for parameters appearing in complex computer models which are expensive to run, and cannot readily be differentiated. This is achieved by connecting the interacting particle system to ensemble Kalman methods for inverse problems. This is joint work with Alfredo Garbuno-Inigo (Caltech), Wuchen Li (UCLA) and Andrew Stuart (Caltech).

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Kalman-Wasserstein Gradient Flows

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