Edge Exclusion Tests for Graphical Model Selection: Complex Gaussian Vectors and Time Series
Edge Exclusion Tests for Graphical Model Selection: Complex Gaussian Vectors and Time Series
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用于图形模型选择的边缘排除测试：复杂高斯向量和时间序列
DOI：
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发表时间：
2019
影响因子：
5.4
通讯作者：
Jitendra Tugnait
中科院分区：
文献类型：
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作者：
Jitendra Tugnait
本文研究了平稳多元高斯时间序列的条件独立图（CIG）的推断问题。一个<inline-formula><tex-math notation="LaTeX">$p $</tex-math></inline-formula>变量高斯时间序列图模型与一个无向图与<inline-formula><tex-math notation="LaTeX">$p$</tex-math></inline-formula>顶点被定义为家庭的时间序列，服从的条件独立的限制所隐含的边集的图。在一些现有的方法中，部分相干性已被用作图形模型选择的检验统计量。为了测试图中给定边的包含/排除，测试以不同的频率应用，需要多次测试并导致测试功率的损失。Matsuda的非参数方法使用Kullback-Leibler散度度量来定义检验统计量，该检验统计量不需要在两个竞争模型之间进行多次检验。在本文中，我们提出了一个广义似然比测试（GLRT）的边缘排除测试统计量，也不需要多次测试。它是计算显着快于松田的方法，模拟表明，我们实现了可比的功率水平。我们提出的方法是基于一种新的制剂的GLRT为基础的边缘排除测试<inline-formula><tex-math notation="LaTeX">$p$</tex-math></inline-formula>-变量复杂高斯图形模型（CGGM），这一结果也是独立的利益。与现有结果的<inline-formula><tex-math notation="LaTeX">$</tex-math></inline-formula><inline-formula><tex-math notation="LaTeX">mathcal {O}（p^5）$</tex-math></inline-formula>相比，建议统计量的计算复杂度为$mathcal {O}（p^3）$。我们还将我们的时间序列图模型选择方法应用于由10个国家的外汇汇率月度趋势组成的外汇数据集。
We consider the problem of inferring the conditional independence graph (CIG) of a stationary multivariate Gaussian time series. A <inline-formula><tex-math notation="LaTeX">$p$</tex-math></inline-formula>-variate Gaussian time series graphical model associated with an undirected graph with <inline-formula><tex-math notation="LaTeX">$p$</tex-math></inline-formula> vertices is defined as the family of time series that obey the conditional independence restrictions implied by the edge set of the graph. In some existing methods, partial coherence has been used as a test statistic for graphical model selection. To test inclusion/exclusion of a given edge in the graph, the test is applied at distinct frequencies, requiring multiple tests and leading to a loss in test power. The nonparametric method of Matsuda uses the Kullback-Leibler divergence measure to define a test statistic which does not need multiple testing to test between two competing models. In this paper we propose a generalized likelihood ratio test (GLRT) based edge exclusion test statistic that also does not need multiple testing. It is computationally significantly faster than the method of Matsuda, and simulations show that we achieve comparable power levels. Our proposed approach is based on a novel formulation of a GLRT based edge exclusion test for <inline-formula><tex-math notation="LaTeX">$p$</tex-math></inline-formula>-variate complex Gaussian graphical models (CGGMs); this result is also of independent interest. The computational complexity of the proposed statistic is <inline-formula><tex-math notation="LaTeX">$mathcal {O}(p^3)$</tex-math></inline-formula> compared to <inline-formula><tex-math notation="LaTeX">$mathcal {O}(p^5)$</tex-math></inline-formula> for the existing result. We also apply our time series graphical model selection method to a foreign exchange data set consisting of monthly trends of foreign exchange rates of 10 countries.
复值时间序列相关性提高了 FMRI 分析的灵敏度。
影响因子：
2.5
作者：
Kociuba,MaryC;Rowe,DanielB
通讯作者：
Rowe,DanielB