Latent Hinge-Minimax Risk Minimization for Inference from a Small Number of Training Samples

Deep Learning (DL) methods show very good performance when trained on large, balanced data sets. However, many practical problems involve imbalanced data sets, or/and classes with a small number of training samples. The performance of DL methods as well as more traditional classifiers drops significantly in such settings. Most of the existing solutions for imbalanced problems focus on customizing the data for training. A more principled solution is to use mixed Hinge-Minimax risk [19] specifically designed to solve binary problems with imbalanced training sets. Here we propose a Latent Hinge Minimax (LHM) risk and a training algorithm that generalizes this paradigm to an ensemble of hyperplanes that can form arbitrary complex, piecewise linear boundaries. To extract good features, we combine LHM model with CNN via transfer learning. To solve multi-class problem we map pre-trained category-specific LHM classifiers to a multi-class neural network and adjust the weights with very fast tuning. LHM classifier enables the use of unlabeled data in its training and the mapping allows for multi-class inference, resulting in a classifier that performs better than alternatives when trained on a small number of training samples.