论文标题
非可逆地更新大都会接受/拒绝决策的统一[0,1]价值
Non-reversibly updating a uniform [0,1] value for Metropolis accept/reject decisions
论文作者
论文摘要
我展示了如何以与统一的[0,1]值（u）的比较来表达大都市接受/拒绝决策，然后作为马尔可夫链状态的一部分，而不是独立对每个迭代进行采样。这为高维度的随机步行都会和兰格文更新提供了较小的改进。当使用持续动量的Langevin更新时，它会产生更大的改进，从而使性能与汉密尔顿蒙特卡罗（HMC）具有长轨迹相当。当某些变量通过其他方法更新时，这很重要，因为如果使用HMC，则只能在轨迹之间进行这些更新，而在Langevin更新中可以更频繁地进行它们。我证明，对于某些连续变量的问题，由HMC或Langevin更新更新，以及离散变量，通过GIBBS对连续变量的更新之间进行采样，Langevin具有持久动量和非可逆更新的langevin，对U的样品的持续更新几乎比HMC高两个。对于贝叶斯神经网络模型也可以看到好处，其中超参数通过吉布斯采样更新。
I show how it can be beneficial to express Metropolis accept/reject decisions in terms of comparison with a uniform [0,1] value, u, and to then update u non-reversibly, as part of the Markov chain state, rather than sampling it independently each iteration. This provides a small improvement for random walk Metropolis and Langevin updates in high dimensions. It produces a larger improvement when using Langevin updates with persistent momentum, giving performance comparable to that of Hamiltonian Monte Carlo (HMC) with long trajectories. This is of significance when some variables are updated by other methods, since if HMC is used, these updates can be done only between trajectories, whereas they can be done more often with Langevin updates. I demonstrate that for a problem with some continuous variables, updated by HMC or Langevin updates, and also discrete variables, updated by Gibbs sampling between updates of the continuous variables, Langevin with persistent momentum and non-reversible updates to u samples nearly a factor of two more efficiently than HMC. Benefits are also seen for a Bayesian neural network model in which hyperparameters are updated by Gibbs sampling.
