Risk-Averse Classification

We develop a new approach to solving classification problems, which is bases on the theory of coherent measures of risk and risk sharing ideas. The proposed approach aims at designing a risk-averse classifier. The new approach allows for associating distinct risk functional to each classes. The risk may be measured by different (non-linear in probability) measures, We analyze the structure of the new classifier design problem and establish its theoretical relation to known risk-neutral design problems. In particular, we show that the risk-sharing classification problem is equivalent to an implicitly defined optimization problem with unequal, implicitly defined but unknown, weights for each data point. We implement our methodology in a binary classification scenario on several different data sets and carry out numerical comparison with classifiers which are obtained using the Huber loss function and other loss functions known in the literature. We formulate specific risk-averse support vector machines in order to demonstrate the viability of our method.