RI: Medium: Quantifying Causality in Distributed Spatial Temporal Brain Networks

脑功能研究的一个关键障碍是，不仅要能够测量哪些信号彼此相关，还要能够测量它们之间的因果关系。相关性量化了线性依赖性，而因果关系能够区分哪个脑区在领导相关的对应区域；因果关系在相关性上画了一个箭头。因果关系是数据分析中的一个难题，本文提出了一种评价因果关系的条件统计依赖的新方法。最终的实际目标是阐明认知加工的原理，并为执行复杂任务的人类受试者提供在线认知反馈。本项目的目标是使用最近开发的基于周期性视觉刺激的脑电图（EEG）量化范例，以提高预先确定的脑电图频带（这里约为10 Hz）上视觉刺激的信噪比。目标是开发基于瞬时频率（希尔伯特变换）的先进信号处理技术，以量化头皮上32个通道视觉刺激的瞬时振幅。一种最近发展的局部统计依赖度量称为相关系数将用于评估在头皮上收集的瞬时振幅时间序列之间的依赖性。相关系数的最大值是统计相关性的度量，这是迈向因果关系的第一步。为了实现因果度量，条件依赖性将通过将相关系数扩展到条件相关系数来评估，首先是变量的三元组，然后是任意维的子空间。相关系数是依赖性的非参数度量；因此，将新方法与在再现核希尔伯特空间中实现的线性和非线性格兰杰因果关系方法进行比较。这些算法将在情感视觉感知研究中从人类受试者收集的数据上进行测试。我们的目标是研究和量化情绪感知的再进入假说——当情绪刺激被感知时，源自高阶皮层的再进入调节负责增强枕叶皮层的激活。这里发展的信号处理和统计方法将提供一种方法来识别在刺激呈现期间依赖的EEG通道和它们之间的因果关系，有效地追踪从受刺激的视觉区域到额叶区域再回到视觉皮层的神经活动流。

A key hurdle in studies of brain function is to be able to measure not only what signals are correlated with one another, but also how they are causally related. Correlation quantifies linear dependence, while causality is capable of distinguishing which brain area is leading the correlated counterparts; causality puts an arrow into correlation. Causality is a difficult problem in data analysis and here a novel measure of conditional statistical dependence to evaluate causality is proposed. The ultimate practical goal is to elucidate the principles of cognitive processing and provide online cognitive feedback to human subjects performing complex tasks. The objective of this project is to use a recently developed paradigm for electroencephalogram (EEG) quantification based on periodic visual stimulation to improve the signal to noise ratio of visual stimulation on a pre-determined EEG frequency band (here around 10 Hz). The goal is to develop advanced signal processing techniques based on instantaneous frequency (Hilbert transform) to quantify the instantaneous amplitude of a visual stimulus in 32 channels over the scalp. A recently developed measure of local statistical dependence in the joint space called correntropy will be utilized to evaluate the dependency among instantaneous amplitude time series collected over the scalp. The maximum value of correntropy is a measure of statistical dependence, which is the first step towards causality. To achieve a causality measure, conditional dependence will be evaluated by extending correntropy to conditional correntropy, first for triplets of variables and them to subspaces of arbitrary dimensions. Correntropy is a nonparametric measure of dependence; hence, the new method will be compared to linear and nonlinear Granger causality methods implemented in reproducing kernel Hilbert spaces.These algorithms will be tested on data collected from human subjects in a study of affective visual perception. The goal is to study and quantify the re-entry hypothesis of emotional perception -- that re-entrant modulation originating from higher-order cortices is responsible for enhanced activation in the occipital cortex when emotionally arousing stimuli are perceived. The signal processing and statistical methods developed here will provide a way to identify dependent EEG channels and causal relationships amongst them during the presentation of the stimulus, effectively tracing the flow of neural activity from the stimulated visual areas to frontal areas and back to the visual cortex.