Ning Lipeng
Department of Psychiatry, Brigham and Women's Hospital, Harvard Medical School.
IEEE Trans Automat Contr. 2020 May;65(5):1901-1910. doi: 10.1109/TAC.2019.2926854. Epub 2019 Jul 4.
This work focuses on the modeling of time-varying covariance matrices using the state covariance of linear systems. Following concepts from optimal mass transport, we investigate and compare three types of covariance paths which are solutions to different optimal control problems. One of the covariance paths solves the Schrödinger bridge problem (SBP). The other two types of covariance paths are based on generalizations of the Fisher-Rao metric in information geometry, which are the major contributions of this work. The general framework is an extension of the approach in [1] which focuses on linear systems without stochastic input. The performances of the three covariance paths are compared using synthetic data and a real-data example on the estimation of dynamic brain networks using functional magnetic resonance imaging.
这项工作专注于使用线性系统的状态协方差对时变协方差矩阵进行建模。遵循最优质量传输的概念，我们研究并比较了三种类型的协方差路径，它们是不同最优控制问题的解。其中一条协方差路径解决薛定谔桥问题（SBP）。另外两种类型的协方差路径基于信息几何中Fisher-Rao度量的推广，这是本工作的主要贡献。一般框架是对[1]中方法的扩展，[1]中的方法专注于没有随机输入的线性系统。使用合成数据和一个关于利用功能磁共振成像估计动态脑网络的真实数据示例，对这三条协方差路径的性能进行了比较。
