Unbiased Hamiltonian Monte Carlo with couplings
Unbiased Hamiltonian Monte Carlo with couplings
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DOI：
10.1093/biomet/asy074
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发表时间：
2017-09
期刊：
影响因子：
2.7
通讯作者：
J. Heng;P. Jacob
中科院分区：
文献类型：
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作者：
J. Heng;P. Jacob
我们提出了一种并行化的哈密顿蒙特卡罗估计的方法。我们的方法涉及到构建一对哈密顿蒙特卡罗链耦合在这样一种方式，他们满足一些随机次数的迭代后。然后可以将这些链组合起来，以便得到的估计量是无偏的。这使得我们可以并行地产生独立的重复，并对它们进行平均，以获得在重复次数限制下一致的估计量，而不是在通常的马尔可夫链迭代次数限制下一致的估计量。我们调查的可扩展性，我们的耦合在高维度上的一个玩具的例子。算法参数的选择和我们提出的方法的效率，然后说明逻辑回归与300协变量和对数高斯考克斯点过程模型与低到细粒度的离散化。
We propose a method for parallelization of Hamiltonian Monte Carlo estimators. Our approach involves constructing a pair of Hamiltonian Monte Carlo chains that are coupled in such a way that they meet exactly after some random number of iterations. These chains can then be combined so that the resulting estimators are unbiased. This allows us to produce independent replicates in parallel and average them to obtain estimators that are consistent in the limit of the number of replicates, rather than in the usual limit of the number of Markov chain iterations. We investigate the scalability of our coupling in high dimensions on a toy example. The choice of algorithmic parameters and the efficiency of our proposed approach are then illustrated on a logistic regression with 300 covariates and a log-Gaussian Cox point processes model with low- to fine-grained discretizations.