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.
