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Statistical and data-driven methodologies have been of growing interest in medical and biomedical applications. In fMRI data analysis, such techniques are helpful for improved understanding of the brain function. Due to finite sample size, future success in this area is limited by two fundamental factors: (a) high dimensionality of the input data and (b) heterogeneous nature of the input data.The main practical motivation for this project is to incorporate various heterogeneous types of information into intelligent data-driven systems for several common fMRI data-analytic problems, such as activation detection and cognitive state classification. Activation detection aims to locate brain regions that are related to a specific cognitive task; cognitive state classification means to infer cognitive states from fMRI images. We aim to improve understanding of different predictive learning approaches appropriate for these problems. To this end, we investigate traditional learning approaches (based on standard inductive learning setting), as well as new emerging learning approaches such as SVM+ and multi-task learning (MTL). For an activation problem, we propose spatial SVM which incorporates two unique characteristics of fMRI data: spatial contiguity and BOLD effect. For the problem of cognitive state classification, we investigate new learning methodology called SVM+ (Vapnik, 2006). SVM+ is a promising approach for heterogeneous fMRI data. However, current understanding of SVM+ is very limited as there are no empirical studies comparing this approach with other existing standard learning methods. In addition, our work extends SVM+ approach to Multi-Task Learning (MTL) setting. This extension leads to a new learning algorithm dubbed svm+MTL. Both SVM+ and svm+MTL have been empirically validated using a real-life fMRI data from a cognitive state classification experiment.