A robust approach based on conditional value-at-risk measure to statistical learning problems
A robust approach based on conditional value-at-risk measure to statistical learning problems
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DOI：
10.1016/j.ejor.2008.07.027
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发表时间：
2009-10
期刊：
影响因子：
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通讯作者：
Akiko Takeda;Takafumi Kanamori
中科院分区：
文献类型：
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作者：
Akiko Takeda;Takafumi Kanamori
在统计学习问题中，观测数据中的测量误差降低了估计的可靠性。有几种方法可以处理观测中的这些不确定性。在本文中，我们提出了使用条件风险价值（CVaR）的措施，以减少测量误差的影响，并研究所产生的CVaR最小化问题和一些现有的方法之间的关系在同一框架。对于包含积分计算的CVaR最小化问题，我们采用MonteCarlo抽样方法，得到了它们的近似解。利用Vapnik和Chervonenkis理论证明了解的逼近误差界和收敛性。数值实验表明，在存在测量误差的情况下，与几种支持向量机相比，CVaR最小化问题可以获得较好的估计结果。
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.