Many applications of machine learning involve sparse high-dimensional data, where the number of input features is (much) larger than the number of data samples, d≫n. Predictive modeling of such data is very ill-posed and prone to overfitting. Several recent studies for modeling high-dimensional data employ new learning methodology called Learning through Contradictions or Universum Learning due to Vapnik (1998,2006). This method incorporates a priori knowledge about application data, in the form of additional Universum samples, into the learning process. This paper investigates generalization properties of the Universum-SVM and how they are related to characteristics of the data. We describe practical conditions for evaluating the effectiveness of Random Averaging Universum.