Support vector regression as conditional value-at-risk minimization with application to financial time-series analysis
Support vector regression as conditional value-at-risk minimization with application to financial time-series analysis
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DOI：
10.1109/mlsp.2010.5589245
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发表时间：
2010-10
期刊：
影响因子：
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通讯作者：
A. Takeda;Jun-ya Gotoh;Masashi Sugiama
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文献类型：
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作者：
A. Takeda;Jun-ya Gotoh;Masashi Sugiama
支持向量机回归(SVR)是机器学习和信号处理中常用的一种回归算法。在本文中，我们首先证明了支持向量机算法等价于最小化ℓ1-损失残差分布的条件风险值(CVaR)，这是一种金融中流行的风险度量。支持向量机与CVaR最小化的等价性使得我们得到了支持向量机的ℓ1-损失泛化误差的一个新的上界。然后，我们证明了在一定条件下，支持向量机实际上最小化了上界，这意味着它是最优性的。最后，将支持向量机方法应用于金融中的指数跟踪问题，提出了一种新的投资组合选择方法。实验表明，与其他方法相比，该方法具有更好的性能。
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.