Stochastic Gradient Hamiltonian Monte Carlo
ثبت نشده
چکیده
Supplementary Material A. Background on Fokker-Planck Equation The Fokker-Planck equation (FPE) associated with a given stochastic differential equation (SDE) describes the time evolution of the distribution on the random variables under the specified stochastic dynamics. For example, consider the SDE: dz = g(z)dt+N (0, 2D(z)dt), (16) where z ∈ R, g(z) ∈ R, D(z) ∈ Rn×n. The distribution of z governed by Eq. (16) (denoted by pt(z)), evolves under the following equation
منابع مشابه
Stochastic Gradient Hamiltonian Monte Carlo with Variance Reduction for Bayesian Inference
Gradient-based Monte Carlo sampling algorithms, like Langevin dynamics and Hamiltonian Monte Carlo, are important methods for Bayesian inference. In large-scale settings, full-gradients are not affordable and thus stochastic gradients evaluated on mini-batches are used as a replacement. In order to reduce the high variance of noisy stochastic gradients, [Dubey et al., 2016] applied the standard...
متن کاملRelativistic Monte Carlo
Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo (MCMC) algorithm that generates proposals for a Metropolis-Hastings algorithm by simulating the dynamics of a Hamiltonian system. However, HMC is sensitive to large time discretizations and performs poorly if there is a mismatch between the spatial geometry of the target distribution and the scales of the momentum distribution....
متن کاملStochastic Gradient Hamiltonian Monte Carlo
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a MetropolisHastings 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 com...
متن کاملAsynchronous Stochastic Gradient MCMC with Elastic Coupling
We consider parallel asynchronous Markov Chain Monte Carlo (MCMC) sampling for problems where we can leverage (stochastic) gradients to define continuous dynamics which explore the target distribution. We outline a solution strategy for this setting based on stochastic gradient Hamiltonian Monte Carlo sampling (SGHMC) which we alter to include an elastic coupling term that ties together multipl...
متن کاملStochastic Gradient Monomial Gamma Sampler
Recent advances in stochastic gradient techniques have made it possible to estimate posterior distributions from large datasets via Markov Chain Monte Carlo (MCMC). However, when the target posterior is multimodal, mixing performance is often poor. This results in inadequate exploration of the posterior distribution. A framework is proposed to improve the sampling efficiency of stochastic gradi...
متن کامل