Corpus ID: 59553458

Understanding MCMC Dynamics as Flows on the Wasserstein Space

@inproceedings{Liu2019UnderstandingMD,
  title={Understanding MCMC Dynamics as Flows on the Wasserstein Space},
  author={Chang Liu and Jingwei Zhuo and J. Zhu},
  booktitle={ICML},
  year={2019}
}
  • 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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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 77 REFERENCES
    MCMC Using Hamiltonian Dynamics
    • 1,623
    • PDF
    A Complete Recipe for Stochastic Gradient MCMC
    • 233
    • Highly Influential
    • PDF
    Riemann manifold Langevin and Hamiltonian Monte Carlo methods
    • 1,013
    • PDF
    Stochastic Gradient Hamiltonian Monte Carlo
    • 431
    • Highly Influential
    • PDF
    Stochastic Gradient Geodesic MCMC Methods
    • 18
    • PDF
    Understanding and Accelerating Particle-Based Variational Inference
    • 15
    • PDF
    Markov Chain Monte Carlo from Lagrangian Dynamics
    • 30
    On the Convergence of Stochastic Gradient MCMC Algorithms with High-Order Integrators
    • 113
    • PDF
    A Unified Particle-Optimization Framework for Scalable Bayesian Sampling
    • 30
    • Highly Influential
    • PDF
    Analysis of Langevin Monte Carlo via Convex Optimization
    • 50
    • PDF