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

研究大脑功能的一个关键障碍是不仅要能够测量哪些信号相互关联，还要能够测量它们之间的因果关系。相关性量化了线性相关性，而因果关系能够区分哪个大脑区域正在领导相关的对应区域;因果关系为相关性注入了一个箭头。因果关系是数据分析中的一个难题，本文提出了一种新的条件统计依赖测度来评价因果关系。最终的实际目标是阐明认知处理的原理，并为执行复杂任务的人类受试者提供在线认知反馈。 该项目的目的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，以提高预定EEG频带（此处约10 Hz）上的视觉刺激的信噪比。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个通道中视觉刺激的瞬时幅度。最近开发的措施，在联合空间称为相关性的局部统计依赖性将被用来评估头皮上收集的瞬时幅度时间序列之间的依赖性。相关熵的最大值是统计相关性的度量，这是走向因果关系的第一步。为了实现因果关系的测量，条件依赖性将通过将相关熵扩展到条件相关熵来评估，首先是三个变量，然后是任意维度的子空间。相关性是一种非参数的依赖性的措施，因此，新的方法将进行比较，线性和非线性格兰杰因果关系的方法实现再生核希尔伯特spaces.These算法将测试从人类受试者的情感视觉感知的研究中收集的数据。我们的目标是研究和量化情绪感知的折返假说--当感知到情绪刺激时，源自高阶皮层的折返调制负责增强枕叶皮层的激活。这里开发的信号处理和统计方法将提供一种方法来识别依赖的EEG通道和它们之间的因果关系，在刺激的呈现过程中，有效地跟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.