Corpus ID: 59553458

Understanding MCMC Dynamics as Flows on the Wasserstein Space

  title={Understanding MCMC Dynamics as Flows on the Wasserstein Space},
  author={Chang Liu and Jingwei Zhuo and J. Zhu},
  • Chang Liu, Jingwei Zhuo, J. Zhu
  • Published in ICML 2019
  • Mathematics, Computer Science
  • It is known that the Langevin dynamics used in MCMC is the gradient flow of the KL divergence on the Wasserstein space, which helps convergence analysis and inspires recent particle-based variational inference methods (ParVIs). But no more MCMC dynamics is understood in this way. In this work, by developing novel concepts, we propose a theoretical framework that recognizes a general MCMC dynamics as the fiber-gradient Hamiltonian flow on the Wasserstein space of a fiber-Riemannian Poisson… CONTINUE READING

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