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Functional Magnetic Resonance Imaging (fMRI) has enabled scientists to look into the active human brain by providing sequences of 3D brain images with intensities representing blood oxygenation level dependent (BOLD) regional activations. This has revealed exciting insights into the spatial and temporal changes underlying a broad range of brain functions. Concomitantly, this new instrumentation has led to a flood of new data: a twenty-minute fMRI session with a single human subject produces a series of 3D brain images each containing approximately 150,000 voxels, collected once a second (or two), yielding tens of millions of data observations. Thus, developing appropriate data analysis methods is needed for truly comprehensive exploration of this ample volume of data. In this dissertation, we contribute a comprehensive framework for exploration of fMRI data, and apply it to a challenging problem: performing classification of hard-to-categorize groups of subjects based on simultaneously recorded brain activation response patterns to behavioral challenges of inhibitory control. Specifically, this dissertation involves the following (progressively more challenging) aims: (i) to develop machine-learning techniques applicable to fMRI contrast maps (static 3D images) to uncover the unique patterns which separate subjects belonging to the different groups; (ii) to explore and develop temporal machine learning methods for fMRI sequences and to extract temporal features to be applied on subject and state classification and (iii) to explore and develop probabilistic graphical models to reveal the functional connectivity and interactivity within brain circuits of inhibitory control. We suggest that through incorporation of computer data analysis principles into functional neuroimaging studies we will be able to identify unique patterns of variability in brain states and deduce about the behavioral probes from the brain activation data (in contrast to the reverse: deducing about brain activation data from behavioral probes). We further propose that this interscientific incorporation may provide a valid tool where objective brain imaging data are used for clinical purpose of classification of psychopathologies and identification of genetic vulnerabilities.