Support vector regression (SVR) is a popular regression algorithm in machine learning and signal processing. In this paper, we first prove that the SVR algorithm is equivalent to minimizing the conditional value-at-risk (CVaR) of the distribution of the ℓ1-loss residuals, which is a popular risk measure in finance. The equivalence between SVR and CVaR minimization allows us to derive a new upper bound on the ℓ1-loss generalization error of SVR. Then we show that SVR actually minimizes the upper bound under some condition, implying its optimality. We finally apply the SVR method to an index tracking problem in finance, and develop a new portfolio selection method. Experiments show that the proposed method compares favorably with alternative approaches.
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