Multi-task support vector machine with pinball loss

With the boom in machine learning, support vector machine (SVM) is widely employed in pattern recognition. However, most of SVM models concentrate on single-task learning, multi-task learning has been largely neglected. Compared with single-task learning, multi-task learning can achieve a good performance for each task by mining the shared information among tasks. In addition, loss function also plays an important role in the accuracy of SVM. Inspired by multi-task learning and the SVM with pinball loss (pin-SVM), we propose two novel multi-task support vector machines with pinball loss for binary classification, named as MTL-pin-SVM I and MTL-pin-SVM II. Both methods maximize the quantile distance for each task, which realizes less sensitive to noise and more stable for re-sampling. Moreover, MTL-pin-SVM II can use different combinations of kernel functions for different tasks, which can get better performance than other multi-task models by choosing the suitable combinations of kernel functions for different tasks. And they include the multi-task SVM with hinge loss as their special cases, which are denoted as MTL-C-SVM I and MTL-C-SVM II. The extensive experiments on multi-task datasets fully validate the validity of the proposed models.