This paper investigates a new learning setting recently introduced by Vapnik  that takes into account a known structure of the training data to improve generalization performance. This setting is a special case of a new inference technology known as Learning with Hidden Information  suitable for many real-life applications with sparse high-dimensional data. We first briefly describe an extension of SVM called SVMγ+  that is associated with this new learning setting, and verify its effectiveness using a synthetic data set. Then we demonstrate the effectiveness of SVMγ+ on a difficult real-life problem: detection of cognitive states from fMRI images obtained from different subjects. These empirical results show that the SVMγ+ approach achieves improved inter-subject generalization vs standard SVM technology.