This paper considers Importance Sampling (IS) for the estimation of tail risks of a loss defined in terms of a sophisticated object such as a machine learning feature map or a mixed integer linear optimisation formulation. Assuming only black-box access to the loss and the distribution of the underlying random vector, the paper presents an efficient IS algorithm for estimating the Value at Risk and Conditional Value at Risk. The key challenge in any IS procedure, namely, identifying an appropriate change-of-measure, is automated with a self-structuring IS transformation that learns and replicates the concentration properties of the conditional excess from less rare samples. The resulting estimators enjoy asymptotically optimal variance reduction when viewed in the logarithmic scale. Simulation experiments highlight the efficacy and practicality of the proposed scheme

翻译：本文审议了估计以机器学习特征图或混合整数线性优化配方等尖端物体界定的损失尾部风险的重要性取样(IS),假设只有黑箱获得损失和基本随机矢量分布,本文提出了估算风险价值和风险条件价值的有效IS算法。任何IS程序中的关键挑战,即确定适当的措施变化,是自动的,通过自建结构的IS转换,从较少的样本中学习和复制条件过剩物的浓度特性。