Input Uncertainty in Support Vector Machines
Support Vector Machines (SVMs) have received much attention over recent years due to a strong motivation from statistical learning theory and excellent empirical results. However, the standard approach cannot accommodate known uncertainties within the input space of the examples. In this work we consider datasets, which in addition to the examples in input space, contain measurements of the uncertainty of these data points. We show that the problem can be reformulated to accommodate such information providing a more robust solution when this information is available. This new problem has a unique solution and the resulting optimisation problem is a Second Order Cone Program (SOCP). In the case when no uncertainty information is available, or the uncertainty is constant across examples, we show that the soluution can be solved using the standard SVM formaulation.