Maanan Saïd, Dumitrescu Bogdan, Giurcăneanu Ciprian Doru
Department of Statistics, University of Auckland, Auckland 1142, New Zealand.
Department of Automatic Control and Computers, University Politehnica of Bucharest, 060042 Bucharest, Romania.
Entropy (Basel). 2018 Jan 19;20(1):76. doi: 10.3390/e20010076.
This work is focused on latent-variable graphical models for multivariate time series. We show how an algorithm which was originally used for finding zeros in the inverse of the covariance matrix can be generalized such that to identify the sparsity pattern of the inverse of spectral density matrix. When applied to a given time series, the algorithm produces a set of candidate models. Various information theoretic (IT) criteria are employed for deciding the winner. A novel IT criterion, which is tailored to our model selection problem, is introduced. Some options for reducing the computational burden are proposed and tested via numerical examples. We conduct an empirical study in which the algorithm is compared with the state-of-the-art. The results are good, and the major advantage is that the subjective choices made by the user are less important than in the case of other methods.
这项工作聚焦于多元时间序列的潜变量图形模型。我们展示了一种原本用于在协方差矩阵的逆矩阵中寻找零点的算法如何进行推广，以便识别谱密度矩阵逆矩阵的稀疏模式。当应用于给定的时间序列时，该算法会产生一组候选模型。采用各种信息论（IT）准则来确定优胜模型。引入了一种针对我们的模型选择问题量身定制的新型IT准则。提出了一些减轻计算负担的选项，并通过数值示例进行了测试。我们进行了一项实证研究，将该算法与当前的先进技术进行了比较。结果良好，主要优点是与其他方法相比，用户做出的主观选择不那么重要。
