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彼此相关，而且还要能够测量它们之间的因果关系。相关性将线性依赖量化，而因果关系能够区分出哪个大脑区域领先于相关的对应者；因果关系为相关性注入了一支箭。因果关系是数据分析中的一个难题，本文提出了一种新的评价因果关系的条件统计相关性度量方法。最终的实践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(EEG)量化范例来提高预定EEG频段(这里约为10赫兹)上视觉刺激的信噪比。我们的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个通道的视觉刺激的瞬时幅度。最近开发的联合空间中的局部统计相关性的度量称为相关熵，将被用来评估在头皮上收集的瞬时幅度时间序列之间的相关性。相关熵的最大值是统计相关性的衡量标准，这是通向因果关系的第一步。为了实现因果关系度量，将通过将条件相关熵扩展到条件相关熵来评估条件相关性，首先是变量的三元组以及它们到任意维度的子空间。相关熵是一种非参数的相关性度量，因此，新方法将与在再生核Hilbert空间中实现的线性和非线性Granger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入假说--当情绪唤醒刺激被感知时，源自高阶大脑皮层的再入调制负责增强枕叶皮质的激活。这里开发的信号处理和统计方法将提供一种方法，在刺激呈现期间识别依赖的EEG通道和它们之间的因果关系，有效地跟踪神经活动从刺激的视觉区域到额叶区域再回到视觉皮质的流动。

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.