Large Scale Imbalanced Classification with Biased Minimax Probability Machine

The biased minimax probability machine (BMPM) constructs a classifier which deals with the imbalanced learning tasks. It provides a worst-case bound on the probability of misclassification of future data points based on reliable estimates of means and covariance matrices of the classes from the training data samples, and achieves promising performance. In this paper, we apply the biased classification model to large scale imbalanced classification problem, and develop a critical extension to train the BMPM efficiently which is a novel training algorithm based on Second Order Cone Programming (SOCP). By removing some crucial assumptions in the original solution to this model, we make the new method more accurate and efficient. We outline the theoretical derivatives of the biased classification model, and reformulate it into a SOCP problem which could be efficiently solved with global optima guarantee. We evaluate our proposed SOCP-based BMPM (BMPMsocp) scheme in comparison with traditional solutions on text classification tasks where negative training documents significantly outnumber the positive ones. Empirical results have shown that our method is more effective and robust to handle imbalanced classification problems than traditional classification approaches.