HMC: Reducing the number of rejections by not using leapfrog and some results on the acceptance rate
HMC: Reducing the number of rejections by not using leapfrog and some results on the acceptance rate
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DOI：
10.1016/j.jcp.2021.110333
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发表时间：
2021-04-13
影响因子：
4.1
通讯作者：
Sanz-Serna, J. M.
中科院分区：
文献类型：
--
作者：
Calvo, M. P.;Sanz-Alonso, D.;Sanz-Serna, J. M.
跃迁积分器通常用于哈密顿蒙特卡罗方法及其变种中。我们给出了强有力的数值证据，证明了在给定的计算工作量下，替代的、易于实现的算法产生的拒绝次数更少。当目标分布的维度很高时，接受的建议的数量可以乘以三倍或更多。被接受提案数量的增加并不是通过损害抽样的任何积极特征来实现的。我们还建立了关于期望接受率和期望能量误差之间单调关系的新的非渐近和渐近结果。这些结果进一步验证了我们所考虑的具有独立意义的积分器之一的推导。(C)2021 Elsevier Inc.保留所有权利。
The leapfrog integrator is routinely used within the Hamiltonian Monte Carlo method and its variants. We give strong numerical evidence that alternative, easy to implement algorithms yield fewer rejections with a given computational effort. When the dimensionality of the target distribution is high, the number of accepted proposals may be multiplied by a factor of three or more. This increase in the number of accepted proposals is not achieved by impairing any positive features of the sampling. We also establish new non-asymptotic and asymptotic results on the monotonic relationship between the expected acceptance rate and the expected energy error. These results further validate the derivation of one of the integrators we consider and are of independent interest. (C) 2021 Elsevier Inc. All rights reserved.