Kramer Mark A, Eden Uri T, Cash Sydney S, Kolaczyk Eric D
Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jun;79(6 Pt 1):061916. doi: 10.1103/PhysRevE.79.061916. Epub 2009 Jun 11.
Networks--collections of interacting elements or nodes--abound in the natural and manmade worlds. For many networks, complex spatiotemporal dynamics stem from patterns of physical interactions unknown to us. To infer these interactions, it is common to include edges between those nodes whose time series exhibit sufficient functional connectivity, typically defined as a measure of coupling exceeding a predetermined threshold. However, when uncertainty exists in the original network measurements, uncertainty in the inferred network is likely, and hence a statistical propagation of error is needed. In this manuscript, we describe a principled and systematic procedure for the inference of functional connectivity networks from multivariate time series data. Our procedure yields as output both the inferred network and a quantification of uncertainty of the most fundamental interest: uncertainty in the number of edges. To illustrate this approach, we apply a measure of linear coupling to simulated data and electrocorticogram data recorded from a human subject during an epileptic seizure. We demonstrate that the procedure is accurate and robust in both the determination of edges and the reporting of uncertainty associated with that determination.
网络——相互作用的元素或节点的集合——在自然和人造世界中比比皆是。对于许多网络而言，复杂的时空动态源于我们未知的物理相互作用模式。为了推断这些相互作用，通常会在那些时间序列表现出足够功能连通性的节点之间添加边，功能连通性通常定义为耦合度量超过预定阈值。然而，当原始网络测量中存在不确定性时，推断出的网络中也可能存在不确定性，因此需要误差的统计传播。在本手稿中，我们描述了一种从多变量时间序列数据推断功能连通性网络的有原则且系统的程序。我们的程序输出推断出的网络以及对最基本关注点的不确定性的量化：边数量的不确定性。为了说明这种方法，我们将线性耦合度量应用于模拟数据以及从一名癫痫发作患者记录的脑电皮质图数据。我们证明该程序在边的确定以及与该确定相关的不确定性报告方面都是准确且稳健的。
