Stochastic Gradient Hamiltonian Monte Carlo

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