L₁ -penalized fraud detection support vector machines

Standard binary classifiers that maximize the overall accuracy fail in fraud detection where very few fraud cases are concealed within a large number of normal ones, as the best accuracy is often achieved by ignoring all fraud cases. In such a scenario, a natural alternative is what we refer to as a fraud-detection support vector machine, which never fails to detect fraud during training. In this article, we propose the L₁-penalized fraud-detection SVM that is capable of efficiently detecting fraud cases and selecting informative variables simultaneously. We establish the piecewise linearity of the L₁-penalized fraud detection SVM as a function of the regularization parameter and then develop an efficient algorithm for computing its entire regularization paths, greatly facilitating its tuning. The advantages of the L₁-penalized fraud detection SVM and its path algorithm for fraud detection are numerically demonstrated using both simulated and real data sets.