论文标题
通过多属性公式从多元依赖时间序列中进行图形学习
Graph Learning from Multivariate Dependent Time Series via a Multi-Attribute Formulation
论文作者
论文摘要
我们考虑推断高维固定多元高斯时间序列的条件独立图（CIG）的问题。在时间序列图中，向量系列的每个组件由不同的节点表示，并且组件之间的关联由相应节点之间的边缘表示。我们将问题提出为随机向量的多属性图估计之一，其中矢量与图形的每个节点相关联。在每个节点上，关联的随机向量由一个时间序列组件及其延迟副本组成。我们提出了一种交替的乘数方向方法（ADMM）解决方案，以最大程度地减少稀疏组套件惩罚的负伪log-logikelihiengood目标函数，以估计与整个多属性图相关的随机向量的精确矩阵。然后从估计的精度矩阵推断时间序列CIG。提供了理论分析。数值结果说明了提出的方法，该方法在正确检测图形边缘时胜过现有的频域方法。
We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node, and associations between components are represented by edges between the corresponding nodes. We formulate the problem as one of multi-attribute graph estimation for random vectors where a vector is associated with each node of the graph. At each node, the associated random vector consists of a time series component and its delayed copies. We present an alternating direction method of multipliers (ADMM) solution to minimize a sparse-group lasso penalized negative pseudo log-likelihood objective function to estimate the precision matrix of the random vector associated with the entire multi-attribute graph. The time series CIG is then inferred from the estimated precision matrix. A theoretical analysis is provided. Numerical results illustrate the proposed approach which outperforms existing frequency-domain approaches in correctly detecting the graph edges.
