Title: Risk-Averse Classification,
Abstract: 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.