发表机构
University of Washington; Sookmyung Women’s University（华盛顿大学; 淑明女子大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种假设精简的推断框架，直接估计高维时间序列逆谱密度之差，建立高斯近似误差界并开发高效算法，用于分析不同条件下网络变化，如脑连接网络。实验验证了方法的有效性。
AI 中文摘要
多变量时间序列的网络分析在许多领域都很流行，从神经科学到地震学。逆谱密度是时间序列网络分析的常见选择，因为它表示在去除所有其他变量的最佳线性预测器后，两个变量之间的频域相关性。在许多应用中，目标是研究这些网络在不同条件下的变化。例如，在神经科学中，人们可能对大脑连接网络在刺激前后如何变化感兴趣。为此，我们开发了一个基于直接估计两个高维逆谱密度之差的推断框架。我们为任何去偏的D-trace估计过程建立了一个新的高斯近似误差界，该界既用于确定Welch谱密度估计器的最优窗口大小，也用于建立我们去偏的D-trace估计器的渐近正态性。此外，我们开发了一种基于广义D-trace估计过程的高效算法，以克服高维推断的计算复杂性。该方法在合成数据实验和脑电图数据实验中得到了验证。
英文摘要
Network analysis for multivariate time series is popular in many fields, from neuroscience to seismology. The inverse spectral density is a common choice for time series network analysis due to its representation of the frequency domain correlation between two variables after removing the best linear predictor of all other variables. In many applications, the goal is to study how these networks change across different conditions. For example, in neuroscience, one might be interested in how the brain connectivity network changes before and after stimulation. Towards this goal, we develop an inference framework based on a direct estimate of the difference in two high-dimensional inverse spectral densities. We develop a new Gaussian approximation error bound for any de-biased D-trace estimation procedure which is then leveraged to both inform optimal window sizes of Welch's estimators of the spectral density and establish asymptotic normality of our de-biased D-trace estimator. Moreover, we develop an efficient algorithm based on a generalized D-trace estimation procedure to overcome the computational complexity of high-dimensional inference. The method is illustrated on synthetic data experiments and on experiments with electroencephalography data.
Comments53 pages, 3 figures
