CVAR公司
离群值
数学
单变量
数学优化
风险度量
下行风险
凸优化
预期短缺
贝尔曼方程
计算机科学
正多边形
统计
风险管理
多元统计
财务
经济
文件夹
几何学
作者
Junyi Liu,Jong-Shi Pang
出处
期刊:Operations Research
[Institute for Operations Research and the Management Sciences]
日期:2023-03-01
卷期号:71 (2): 397-414
被引量:3
标识
DOI:10.1287/opre.2021.2248
摘要
For the treatment of outliers, the paper “Risk-Based Robust Statistical Learning by Stochastic Difference-of-Convex Value-Function Optimization” by Junyi Liu and Jong-Shi Pang proposes a risk-based robust statistical learning model. Employing a variant of the conditional value-at-risk risk measure, called the interval conditional value-at-risk (In-CVaR), the model aims to exclude the risks associated with the left and right tails of the loss. The resulting nonsmooth and nonconvex model considers the population In-CVaR risk and distinguishes the upside and downside losses with asymmetric weights. For the solution of the model in both regression and classification, the authors show that the objective function is the difference of two convex functions each being the optimal objective value of a univariate convex stochastic program. A sampling and convex programming-based algorithm is developed with the appropriate control of incremental sample sizes, and its subsequential almost-sure convergence to a critical point is established. Numerical results illustrate the practical performance of the model and methodology.
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