A Complete Recipe for Stochastic Gradient MCMC
Yian Ma, Tianqi Chen, Emily B. Fox

Citation
Yian Ma, Tianqi Chen, Emily B. Fox. "A Complete Recipe for Stochastic Gradient MCMC". Neural Information Processing Systems, 7, December, 2015.

Abstract
Many recent Markov chain Monte Carlo (MCMC) samplers leverage stochastic dynamics with state adaptation to define a Markov transition kernel that efficiently explores a target distribution. In tandem, a focus has been on devising scalable MCMC algorithms via data subsampling and using stochastic gradients in the stochastic dynamic simulations. However, such stochastic gradient MCMC methods have used simple stochastic dynamics, or required significant physical intuition to modify the dynamical system to account for the stochastic gradient noise. In this paper, we provide a general recipe for constructing MCMC samplers--including stochastic gradient versions--based on continuous Markov processes specified via two matrices. We constructively prove that the framework is complete. That is, any continuous Markov process that provides samples from the target distribution can be written in our framework. We demonstrate the utility of our recipe by trivially "reinventing" previously proposed stochastic gradient MCMC samplers, and in proposing a new state-adaptive sampler: stochastic gradient Riemann Hamiltonian Monte Carlo (SGRHMC). Our experiments on simulated data and a streaming Wikipedia analysis demonstrate that the proposed sampler inherits the benefits of Riemann HMC, with the scalability of stochastic gradient methods.

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• HTML

  Yian Ma, Tianqi Chen, Emily B. Fox. <a
  href="http://www.terraswarm.org/pubs/646.html"
  >A Complete Recipe for Stochastic Gradient
  MCMC</a>, Neural Information Processing Systems, 7,
  December, 2015.

• Plain text

  Yian Ma, Tianqi Chen, Emily B. Fox. "A Complete Recipe
  for Stochastic Gradient MCMC". Neural Information
  Processing Systems, 7, December, 2015.

• BibTeX

  @inproceedings{MaChenFox15_CompleteRecipeForStochasticGradientMCMC,
      author = {Yian Ma and Tianqi Chen and Emily B. Fox},
      title = {A Complete Recipe for Stochastic Gradient MCMC},
      booktitle = {Neural Information Processing Systems},
      day = {7},
      month = {December},
      year = {2015},
      abstract = {Many recent Markov chain Monte Carlo (MCMC)
                samplers leverage stochastic dynamics with state
                adaptation to define a Markov transition kernel
                that efficiently explores a target distribution.
                In tandem, a focus has been on devising scalable
                MCMC algorithms via data subsampling and using
                stochastic gradients in the stochastic dynamic
                simulations. However, such stochastic gradient
                MCMC methods have used simple stochastic dynamics,
                or required significant physical intuition to
                modify the dynamical system to account for the
                stochastic gradient noise. In this paper, we
                provide a general recipe for constructing MCMC
                samplers--including stochastic gradient
                versions--based on continuous Markov processes
                specified via two matrices. We constructively
                prove that the framework is complete. That is, any
                continuous Markov process that provides samples
                from the target distribution can be written in our
                framework. We demonstrate the utility of our
                recipe by trivially "reinventing" previously
                proposed stochastic gradient MCMC samplers, and in
                proposing a new state-adaptive sampler: stochastic
                gradient Riemann Hamiltonian Monte Carlo (SGRHMC).
                Our experiments on simulated data and a streaming
                Wikipedia analysis demonstrate that the proposed
                sampler inherits the benefits of Riemann HMC, with
                the scalability of stochastic gradient methods.},
      URL = {http://terraswarm.org/pubs/646.html}
  }
  

Posted by Emily B. Fox on 8 Oct 2015.
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