A Real-Time Fully-Parallel Alternative to MCMC

MCMC 的实时全并行替代方案

• 批准号: 1946660
• 金额: --
• 依托单位: University of Liverpool
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1946660
• 关键词: Real; Time; Fully; Parallel; Alternative

This PhD aims to investigate Sequential Monte Carlo (SMC) samplers as an alternative to Markov chain Monte Carlo (MCMC) in the context of Bayesian inference.MCMC is a numerical Bayesian method that allows high-fidelity physical models to be combined with data to make inferences in the presence of pronounced uncertainty. Improvements to MCMC have historically focused on algorithmic advances, involving, for example, the use of local gradient information and of gradually migrating from an easy reference problem to the problem of interest. Particularly with these improvements, MCMC is an effective solution to the vast number of problems that can be posed as inferences involving data using statistical models. In the context of any one problem, bespoke optimisation can be used to exploit the available (parallel) computational resources. However, because MCMC fundamentally uses the evolution of a single Markov- Chain to convey uncertainty, such optimisation is necessarily problem-specific. There is therefore little scope to develop a generic MCMC implementation that fully exploits parallel processing architectures. As a result, the ability of MCMC to provide solutions to next-generation problems is limited.SMC samplers can solve the same problems as MCMC. In contrast to MCMC, SMC samplers use the diversity of a population of samples to convey uncertainty. For the majority of the operation of an SMC sampler, each sample is processed independently. This makes it trivial to parallelise the majority of the SMC sampler. However, at a specific point in the SMC sampler, it becomes necessary to perform a "resampling" step. A text-book implementation of this resampling step is impossible to parallelise in a scalable fashion. However, previous research has demonstrated that it is possible to implement the resampling operation using a divide-and-conquer strategy. In so doing, it becomes possible to parallelise the resampling step.This project has two key objectives: to apply SMC samplers to real-world problems and to explore the theoretical differences of SMC samplers relative to MCMC. The real-world problems will exist in the sphere of defence and security, in which context combining runtime efficiency with accurate estimation is very important. The SMC samplers applied to these problems will fully exploit the computational power of modern and next generation many-core architectures and systems (such as multicore CPUs, GPUs, Xeon Phis and super-computing clusters). The goal of the theoretical investigations is to identify further unique mathematical characteristics of SMC samplers that allow them to outperform MCMC samplers by an even more significant margin. These investigations will not be limited to but will include looking at sample correlations, optimised l-kernels, time-irreversible proposals, non-markovian proposals, and changing targets.To carry out the project, the student will need to reason about mathematical ideas, implement algorithms in software, and run simulations to assess algorithmic performance.This project falls under EPSRC's Mathematical Sciences theme and its Statistics and Applied Probability research area.

本博士旨在研究序贯蒙特卡罗（SMC）采样器作为贝叶斯推断背景下马尔可夫链蒙特卡罗（MCMC）的替代方案。MCMC是一种数值贝叶斯方法，允许高保真物理模型与数据相结合，在存在明显不确定性的情况下进行推断。MCMC的改进历来集中在算法的进步上，例如，涉及局部梯度信息的使用以及从简单的参考问题逐渐迁移到感兴趣的问题。特别是这些改进，MCMC是一个有效的解决方案，可以提出大量的问题，涉及使用统计模型的数据推断。在任何一个问题的上下文中，定制优化可以用来利用可用的（并行）计算资源。然而，由于MCMC从根本上使用单个马尔可夫链的演化来传达不确定性，因此这种优化必然是特定于问题的。因此，几乎没有空间来开发一个通用的MCMC实现，充分利用并行处理架构。因此，MCMC为下一代问题提供解决方案的能力是有限的。SMC采样器可以解决与MCMC相同的问题。与MCMC相比，SMC采样器使用样本群体的多样性来传达不确定性。对于SMC采样器的大部分操作，每个样品都是独立处理的。这使得并行化SMC采样器的大部分变得微不足道。然而，在SMC取样器中的特定点处，有必要执行“重新取样”步骤。这个重新排序步骤的教科书实现不可能以可扩展的方式并行化。然而，以前的研究表明，它是可能的，以实现使用分治策略的恢复操作。这个项目有两个主要目标：将SMC采样器应用于现实世界的问题，并探索SMC采样器相对于MCMC的理论差异。现实世界的问题将存在于防御和安全领域，在这种情况下，将运行时效率与准确的估计相结合是非常重要的。应用于这些问题的SMC采样器将充分利用现代和下一代众核架构和系统（如多核CPU，GPU，Xeon Phis和超级计算集群）的计算能力。理论研究的目标是进一步确定SMC采样器的独特数学特性，使它们能够以更显著的幅度优于MCMC采样器。这些调查将不仅限于，但将包括查看样本相关性，优化的l-内核，时间不可逆的建议，非马尔可夫建议，和不断变化的目标。要执行该项目，学生将需要对数学思想的原因，在软件中实现算法，并运行模拟来评估算法性能。该项目福尔斯EPSRC的数学科学主题及其统计和应用概率研究领域。