Joint Association Graph Screening and Decomposition for Large-scale Linear Dynamical Systems
This work addresses efficient network learning for large-scale systems like stock markets and gene regulatory networks, but it appears incremental as it builds on existing graphical methods with joint regularization.
The paper tackles the problem of learning large-scale linear dynamical networks by introducing a joint graphical screening and estimation (JGSE) framework that pre-determines unnecessary edges and decomposes networks into smaller subnetworks, reducing problem size and search space. Experiments on synthetic and real-world data demonstrate its effectiveness in network topology identification and dynamics estimation.
This paper studies large-scale dynamical networks where the current state of the system is a linear transformation of the previous state, contaminated by a multivariate Gaussian noise. Examples include stock markets, human brains and gene regulatory networks. We introduce a transition matrix to describe the evolution, which can be translated to a directed Granger transition graph, and use the concentration matrix of the Gaussian noise to capture the second-order relations between nodes, which can be translated to an undirected conditional dependence graph. We propose regularizing the two graphs jointly in topology identification and dynamics estimation. Based on the notion of joint association graph (JAG), we develop a joint graphical screening and estimation (JGSE) framework for efficient network learning in big data. In particular, our method can pre-determine and remove unnecessary edges based on the joint graphical structure, referred to as JAG screening, and can decompose a large network into smaller subnetworks in a robust manner, referred to as JAG decomposition. JAG screening and decomposition can reduce the problem size and search space for fine estimation at a later stage. Experiments on both synthetic data and real-world applications show the effectiveness of the proposed framework in large-scale network topology identification and dynamics estimation.