CAREER: Sequential Monte Carlo Methods for High Dimensional Systems

职业：高维系统的序贯Monte Carlo方法研究高维系统的序贯Monte Carlo方法的进展对于生物学、气象学、经济学、社会科学和工程学等不同学科都具有重要的意义。这些系统的特点是非线性和难以理解。由简单的局部规则控制的计算方法有可能提供有洞察力的解释，并为定量和定性描述和理解复杂系统铺平道路。本项目的重点是发展这种方法，特别是在顺序蒙特卡罗中发展协同研究和教育计划。基于信号处理的高维系统，本研究的目的是奠定了高维系统的序贯蒙特卡罗方法的基础。在文献中，有声称粒子滤波器不能用于复杂系统，因为它们的随机测量退化为单个粒子。虽然这对于这些过滤器的标准实现是正确的，但对于替代方法则不成立。提出了一种基于分而治之原则的新方法。特别是，通过设置一个相互连接的过滤器网络，避免了传统粒子过滤的崩溃，每个过滤器都工作在低维空间。研究任务包括开发方法的理论基础，制定从业人员使用的指导方针，分析其准确性，稳定性和可扩展性，并在广泛的复杂系统上进行验证。所提出的方法是原创的，并提供了解决方案，可以说是最大的开放问题的粒子滤波。

CAREER: Sequential Monte Carlo Methods for High Dimensional SystemsAbstractAdvances in the development of models and methods that can satisfactorily describe and analyze high dimensional systems are extremely valuable for many different disciplines including biology, meteorology, economics,social sciences, and engineering. These systems are characterized by nonlinearities and are difficult to understand.Computational methods governed by simple local rules have the potential of providing insightful interpretationsand of paving the way towards quantitative and qualitative descriptions and understanding of complex systems.This project is focused on development of such methods and in particular on the development of a synergistic research and educational program in sequential Monte Carlo-based signal processing for high dimensional systems.This research aims at laying the foundations of a sequential Monte Carlo methodology for high dimensional systems. In the literature, there are claims stating that particle filters cannot be used for complex systems because their random measures degenerate to single particles. While this is true for standard implementation of these filters, it does not hold true for alternative approaches. A new methodology based on the principle of divide and conquer is developed. In particular, the collapse of traditional particle filltering is avoided by setting an interconnected network of filters, each of them working on lower dimensional spaces. Research tasks include development of the theoretical grounds of the methods, establishment of guidelines for its use by practitioners,analysis of its accuracy, stability and scalability, and validation on a wide range of complex systems. The proposed methods are original and provide solutions to arguably the biggest open problem of particle filtering.