Convex optimization methods for system identification and graphical modeling of time series

系统辨识和时间序列图形建模的凸优化方法

• 批准号: 1128817
• 负责人: Lieven Vandenberghe
• 金额: $ 37.88万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1128817&HistoricalAwards=false
• 关键词: Convex; optimization; methods; system; identification

ObjectivesThe project aims at developing new methods for dynamical system modeling, based on convex optimization formulations and recent algorithms for large-scale non-smooth optimization. A first component of the project addresses the estimation and topology selection of graphical models of time series. A graphical model provides a graph representation of relations between random variables, for example, conditional dependence. These relations can be translated into sparsity constraints on the parameters of the model. A fundamental challenge in the estimation of a graphical model is the selection of a sparse graph topology from observed data. The project aims at developing methods for sparse topology selection via non-smooth convex regularizations. The main application that motivates this work is connectivity analysis from functional magnetic resonance imaging time series. A second part is concerned with new methods for system identification based on convex algorithms for low-rank approximation of structured matrices. This work requires the formulation of system identification problems as constrained rank optimization problems and the development of large-scale algorithms for convex relaxations of the rank optimization problems.Intellectual MeritThe project combines techniques from optimization, system theory, and machine learning to address fundamental problems in the modeling of dynamical systems.Graphical models, an important topic in machine learning, are not widely studied in system identification. Conversely, system identification can provide tools for modeling dynamical aspects in machine learning problems. The use of convex formulations and fast first-order algorithms will enable an efficient solution of large instances in practical applications.Broader ImpactsSoftware implementations of the algorithms developed in the project will be made freely available. The outcomes will be integrated in the graduate optimization sequence in the Electrical Engineering Department at UCLA, in particular an advanced course on large-scale optimization. Research opportunities will be offered to students via individual study courses and summer internships.

ObjectivesThe项目的目的是开发新的方法，动力系统建模，凸优化配方和最近的大规模非光滑优化算法的基础上。 该项目的第一个组成部分解决了时间序列图形模型的估计和拓扑选择。 图形模型提供了随机变量之间关系的图形表示，例如条件依赖。 这些关系可以转化为对模型参数的稀疏约束。 一个基本的挑战，在估计的图形模型是选择一个稀疏的图形拓扑结构从观察到的数据。 该项目旨在通过非光滑凸正则化开发稀疏拓扑选择方法。 激励这项工作的主要应用是从功能磁共振成像时间序列的连接分析。第二部分是关于基于结构矩阵低秩近似的凸算法的系统辨识新方法。 该项目将系统辨识问题表述为约束秩优化问题，并开发用于秩优化问题的凸松弛的大规模算法。智力优势该项目结合了优化、系统理论和机器学习的技术，以解决动态系统建模中的基本问题。图形模型是机器学习中的一个重要课题，在系统辨识中尚未得到广泛研究。 相反，系统识别可以为机器学习问题中的动态方面建模提供工具。凸公式和快速一阶算法的使用将使实际应用中的大型实例的有效解决方案成为可能。更广泛的影响项目中开发的算法的软件实现将免费提供。研究结果将被整合到加州大学洛杉矶分校电气工程系的研究生优化序列中，特别是关于大规模优化的高级课程。 研究机会将通过个人学习课程和暑期实习提供给学生。