A fundamental problem in many science and engineering disciplines is inferring the characteristics of a physical or biological system from the dependencies in data recorded from the system. The dependencies in data, particularly in case of signals recorded from brain, are commonly believed to be nonlinear and the underlying model is often unknown. This thesis focusses on developing novel information-theoretic approaches to detect and quantify spectral and spatiotemporal dependencies from data in a data-driven manner and applies them to electrocorticographic (ECoG) recordings from epilepsy patients to unravel epileptic brain networks. Frequency components in a signal or between two signals, not necessarily at the same frequency, are spectrally dependent if they are not statistically independent. Two signals are temporally dependent if the past measurements at one decrease the uncertainty in predicting the other.

First, we define a novel metric, mutual information in frequency, to detect spectral dependency and quantify it using a data-driven estimator. We then develop a data-driven estimator of mutual information between dependent data using mutual information in frequency. Next, we develop a model-based and a data-driven estimator of directed information to detect and quantify the temporal dependencies in data. Finally, we apply the proposed metrics to ECoG recordings from epilepsy patients to identify seizure onset zone (SOZ), to learn the spatiotemporal characteristics of seizures and to infer the cross-frequency coupling in SOZ. We observe that seizure onset zone drives the rest of brain to a seizure during pre-seizure and seizure periods, while it acts as a sink during post-seizure periods. In addition, high frequency coupling increases during seizures within an ECoG channel and between channels in the same anatomical region in SOZ, but not between different regions in SOZ. This suggests different anatomical regions in the SOZ are independently driving the seizure activity and any treatment should potentially target these regions simultaneously. Going forward, the dependencies unraveled by the proposed metrics should be further analyzed to optimize the parameters of closed-loop electrical stimulation based treatments for epilepsy.