This thesis concerns a novel approach to addressing the issue of class imbalance in machine learning, in particular by modifying the sampling technique itself. Through the use of convex optimization, statistical learning theory, and numerical simulation, the technique of Nomination Sampling is applied to the Logistic regression and Support Vector Machine classifiers to obtain a better training set. Further, this sampling technique is based off of expert opinion, which until now has received only minimal attention in the machine learning community.

Efficient algorithms for solving the proposed learning problems are given, and numerical studies are performed to validate the efficacy of the methods presented.