A CVaR-Based Programming for Support Vector Machine with Uncertain Information

For the parallel support vector machine problem with uncertain information on the observation, by characterizing the violation of the positive class training data to the “upper” support hyperplane and that of the negative class training data to the “lower” support hyperplane via the conditional value-at-risk (CVaR), we establish a CVaR-based optimization model. For the model, we first show that it is a good convex approximation to the basic chance-constrained optimization model for the problem, then with the help of Lagrange duality theory, we transform it into a deterministic semi-definite programming (SDP) which can be numerically solved by the state-of-the-art SDP solvers. Numerical experiments conducted on the artificial and the real benchmark datasets show the validity and the efficiency of the proposed model.