There has been a dramatic increase in application of statistical and machine learning methods for predictive data-analytic modeling of biomedical data. Most existing work in this area involves application of standard supervised learning techniques. Typical methods include standard classification or regression techniques, where the goal is to estimate an indicator function (classification decision rule) or real-valued function of input variables, from finite training sample. However, real-world data often contain additional information besides labeled training samples. Incorporating this additional information into learning (model estimation) leads to nonstandard/advanced learning formalizations that represent extensions of standard supervised learning. Recent examples of such advanced methodologies include semi-supervised learning (or transduction) and learning through contradiction (or Universum learning). This thesis investigates two new advanced learning methodologies along with their biomedical applications. The first one is motivated by modeling complex survival data which can incorporate future, censored, or unknown data, in addition to (traditional) labeled training data. Here we propose original formalization for predictive modeling of survival data, under the framework of Learning Using Privileged Information (LUPI) proposed by Vapnik. Survival data represents a collection of time observations about events. Our modeling goal is to predict the state (alive/dead) of a subject at a pre-determined future time point. We explore modeling of survival data as binary classification problem that incorporates additional information (such as time of death, censored/uncensored status, etc.) under LUPI framework. Then we propose two advanced constructive Support Vector Machine (SVM)-based formulations: SVM+ and Loss-Order SVM (LO-SVM). Empirical results using simulated and real-life survival data indicate that the proposed LUPI-based methods are very effective (versus classical Cox regression) when the survival time does not follow classical probabilistic assumptions. Second advanced methodology investigates a new learning paradigm for classification called Group Learning. This approach is motivated by modeling high-dimensional data when the number of input features is much larger than the number of training samples. There are two main approaches to solving such ill-posed problems: (a) selecting a small number of informative features via feature selection; (b) using all features but imposing additional complexity constraints, e.g., ridge regression, SVM, LASSO, etc. The proposed Group Learning method takes a different approach, by splitting all features into many (t) groups, and then estimating a classifier in reduced space (of dimensionality d/t). This approach effectively uses all features, but implements training in a lower-dimensional input space. Note that the formation of groups reflects application-domain knowledge. For example, in classifying of two-dimensional images represented as a set of pixels (original high-dimensional input space), appropriate groups can be formed by grouping adjacent pixels or “local patches” because adjacent pixels are known to be highly correlated. We provide empirical validation of this new methodology for two real-life applications: (a) handwritten digit recognition, and (b) predictive classification of univariate signals, e.g., prediction of epileptic seizures from intracranial electroencephalogram (iEEG) signal. Prediction of epileptic seizures is particularly challenging, due to highly unbalanced data (just 4–5 observed seizures) and patient-specific modeling. In a joint project with Mayo Clinic, we have incorporated the Group Learning approach into an SVM-based system for seizure prediction. This system performs subject-specific modeling and achieves robust prediction performance.