Citation
Tianqi Chen, Emily B. Fox, Carlos Guestrin. "Stochastic Gradient Hamiltonian Monte Carlo". International Conference on Machine Learning, 21, June, 2014.

Abstract
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis- Hastings framework, enabling more efficient exploration of the state space than standard random-walk proposals. The popularity of such methods has grown significantly in recent years. However, a limitation of HMC methods is the required gradient computation for simulation of the Hamiltonian dynamical system -- such a computation is infeasible in problems involving a large sample size or streaming data. Instead, we must rely on a noisy gradient estimate computed from a subset of the data. In this paper, we explore the properties of such a stochastic gradient HMC approach. Surprisingly, the natural implementation of the stochastic approximation can be arbitrarily bad. To address this problem we introduce a variant that uses second-order Langevin dynamics with a friction term that counteracts the effects of the noisy gradient, maintaining the desired target distribution as the invariant distribution. Results on simulated data validate our theory. We also provide an application of our methods to a classification task using neural networks and to online Bayesian matrix factorization.

Electronic downloads

• https://www.src.org/library/publication/p070001/. (Link to publication on SRC website.)
• http://arxiv.org/pdf/1402.4102v2.pdf

• HTML

  Tianqi Chen, Emily B. Fox, Carlos Guestrin. <a
  href="http://www.terraswarm.org/pubs/307.html"
  >Stochastic Gradient Hamiltonian Monte Carlo</a>,
  International Conference on Machine Learning, 21, June, 2014.

• Plain text

  Tianqi Chen, Emily B. Fox, Carlos Guestrin. "Stochastic
  Gradient Hamiltonian Monte Carlo". International
  Conference on Machine Learning, 21, June, 2014.

• BibTeX

  @inproceedings{ChenFoxGuestrin14_StochasticGradientHamiltonianMonteCarlo,
      author = {Tianqi Chen and Emily B. Fox and Carlos Guestrin},
      title = {Stochastic Gradient Hamiltonian Monte Carlo},
      booktitle = {International Conference on Machine Learning},
      day = {21},
      month = {June},
      year = {2014},
      abstract = {Hamiltonian Monte Carlo (HMC) sampling methods
                provide a mechanism for defining distant proposals
                with high acceptance probabilities in a
                Metropolis- Hastings framework, enabling more
                efficient exploration of the state space than
                standard random-walk proposals. The popularity of
                such methods has grown significantly in recent
                years. However, a limitation of HMC methods is the
                required gradient computation for simulation of
                the Hamiltonian dynamical system -- such a
                computation is infeasible in problems involving a
                large sample size or streaming data. Instead, we
                must rely on a noisy gradient estimate computed
                from a subset of the data. In this paper, we
                explore the properties of such a stochastic
                gradient HMC approach. Surprisingly, the natural
                implementation of the stochastic approximation can
                be arbitrarily bad. To address this problem we
                introduce a variant that uses second-order
                Langevin dynamics with a friction term that
                counteracts the effects of the noisy gradient,
                maintaining the desired target distribution as the
                invariant distribution. Results on simulated data
                validate our theory. We also provide an
                application of our methods to a classification
                task using neural networks and to online Bayesian
                matrix factorization.},
      URL = {http://terraswarm.org/pubs/307.html}
  }
  

Posted by Barb Hoversten on 27 Apr 2014.
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