Allocating computation over multiple chains to reduce sampling time in MCMC is crucial in making MCMC more applicable in the state of the art models such as deep neural networks. One of the parallelization schemes for MCMC is partitioning the sample space to run different MCMC chains in each component of the partition (VanDerwerken and Schmidler in Parallel Markov chain Monte Carlo. arXiv:1312.7479, 2013; Basse et al. in Artificial intelligence and statistics, pp 1318–1327, 2016). In this work, we take Basse et al. (2016)’s bridge sampling approach and apply constrained Hamiltonian Monte Carlo on partitioned sample spaces. We propose a random dimension partition scheme that combines well with the constrained HMC. We empirically show that this approach can expedite MCMC sampling for any unnormalized target distribution such as Bayesian neural network in a high dimensional setting. Furthermore, in the presence of multi-modality, this algorithm is expected to be more efficient in mixing MCMC chains when proper partition elements are chosen.

中文翻译：

---

划分样本空间的哈密顿马尔可夫链蒙特卡罗方法及其在贝叶斯深度神经网络中的应用

在多条链上分配计算以减少MCMC中的采样时间对于使MCMC更适用于现有模型（如深度神经网络）至关重要。MCMC的并行化方案之一是在分区的每个组件中划分样本空间以运行不同的MCMC链（并行Markov链Monte Carlo中的VanDerwerken和Schmidler。arXiv：1312.7479，2013； Basse等人，人工智能与统计， pp 1318–1327，2016年）。在这项工作中，我们采用Basse等。（2016年）的桥梁抽样方法，并在分区样本空间上应用了受约束的哈密顿量蒙特卡罗方法。我们提出了一种与约束HMC很好结合的随机尺寸划分方案。我们的经验表明，这种方法可以加快任何未归一化的目标分布（例如在高维环境中的贝叶斯神经网络）的MCMC采样。此外，在多模态的情况下，该算法预计将在混合MCMC链当被选择适当的隔离元件更有效。