Robust BMPM training based on second-order cone programming and its application in medical diagnosis.

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 develop a novel yet critical extension training algorithm for BMPM that is based on Second-Order Cone Programming (SOCP). Moreover, we apply the biased classification model to medical diagnosis problems to demonstrate its usefulness. By removing some crucial assumptions in the original solution to this model, we make the new method more accurate and robust. We outline the theoretical derivatives of the biased classification model, and reformulate it into an 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 medical diagnosis tasks where the objectives are to focus on improving the sensitivity (the accuracy of the more important class, say "ill" samples) instead of the overall accuracy of the classification. Empirical results have shown that our method is more effective and robust to handle imbalanced classification problems than traditional classification approaches, and the original Fractional Programming-based BMPM (BMPMFP).