论文标题
量身定制尾巴：细粒尾巴灵敏度的风险措施
Tailoring to the Tails: Risk Measures for Fine-Grained Tail Sensitivity
论文作者
论文摘要
预期风险最小化（ERM）是许多机器学习系统的核心。这意味着使用单个数字（其平均值）总结了损失分布中固有的风险。在本文中，我们提出了一种构建风险措施的一般方法，该方法表现出所需的尾巴敏感性，并可能取代ERM中的期望操作员。我们的方法依赖于具有所需尾巴行为的参考分布的规范，该分布是与连贯上层概率一对一的对应关系。与此上层概率兼容的任何风险度量都会显示出尾部灵敏度，该灵敏度可很好地调整为参考分布。作为一个具体的例子，我们专注于基于F-Divergence歧义集的分歧风险度量，这是一种用于促进机器学习系统的分布鲁棒性的广泛工具。例如，我们展示了基于kullback-leibler差异的歧义集与次指定随机变量的类别相关。我们阐述了差异风险度量和重新排列不变的Banach规范的联系。
Expected risk minimization (ERM) is at the core of many machine learning systems. This means that the risk inherent in a loss distribution is summarized using a single number - its average. In this paper, we propose a general approach to construct risk measures which exhibit a desired tail sensitivity and may replace the expectation operator in ERM. Our method relies on the specification of a reference distribution with a desired tail behaviour, which is in a one-to-one correspondence to a coherent upper probability. Any risk measure, which is compatible with this upper probability, displays a tail sensitivity which is finely tuned to the reference distribution. As a concrete example, we focus on divergence risk measures based on f-divergence ambiguity sets, which are a widespread tool used to foster distributional robustness of machine learning systems. For instance, we show how ambiguity sets based on the Kullback-Leibler divergence are intricately tied to the class of subexponential random variables. We elaborate the connection of divergence risk measures and rearrangement invariant Banach norms.
