A robust approach based on conditional value-at-risk measure to statistical learning problems

In statistical learning problems, measurement errors in the observed data degrade the reliability of estimation. There exist several approaches to handle those uncertainties in observations. In this paper, we propose to use the conditional value-at-risk (CVaR) measure in order to depress influence of measurement errors, and investigate the relation between the resulting CVaR minimization problems and some existing approaches in the same framework. For the CVaR minimization problems which include the computation of integration, we apply Monte Carlo sampling method and obtain their approximate solutions. The approximation error bound and convergence property of the solution are proved by Vapnik and Chervonenkis theory. Numerical experiments show that the CVaR minimization problem can achieve fairly good estimation results, compared with several support vector machines, in the presence of measurement errors.