Understanding how a neuron processes information and communicates with other neurons is key to unravel the brain's mechanisms underlying perception, learning and motor processing. Key to characterize neurons acting in concert is the ability to simultaneously measure their firing patterns in awake behaving subjects. Microelectrode arrays (MEAs) implanted in the brain allow simultaneous monitoring of the activity of large ensembles of cells while subjects carry out specific tasks. Isolating the spike pattern characterizing each cell's signature firing requires sophisticated signal processing algorithms, particularly to track the nonstationary behavior of these waveforms over extended periods of time. In this thesis, we introduce a compressive spike sorting technique that discriminates spike patterns from individual neurons using a sparse representation of the ensemble raw data. An iterative learning algorithm is introduced to estimate and adapt a set of optimal thresholds that maximize the separability between spike classes while minimizing the average waveform reconstruction error. Once derived, spike trains are then used to infer functional connectivity patterns among the recorded neural ensemble constituents. We introduce two information-theoretic approaches within the realm of graphical models that capture the spatiotemporal dependency between neurons' spiking patterns. Specifically, the class of spatiotemporal maximum entropy models is shown to incorporate higher-order interactions. We demonstrate the richness of these techniques in improving our understanding of neural function and dysfunction at the millisecond and micron resolutions, and their potential to be applied in emerging applications of brain machine interface technology to help improve the lifestyle of people with severe disabilities.
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