AI 中文总结
该研究提出自相似生成估计（SS-GEN）方法，利用渐近尾部结构，将尾部学习转化为紧凑域问题，由深度生成模型处理，能模拟多元尾部事件、估计罕见事件概率，在多种分布下有渐近精确性，优于现有方法。
AI 中文摘要
我们引入了自相似生成估计（SS-GEN），这是一种在重尾和轻尾情况下模拟多元尾部事件并估计罕见事件概率的方法。SS-GEN利用渐近尾部结构将尾部分布分解为一个明确的径向分量和一个非参数角向分量，将尾部学习简化为一个可由现成深度生成模型处理的紧凑域问题。由此产生的采样器生成具有代表性的极端场景，并支持远超观测数据的概率估计。在温和的非参数尾部假设下，我们表明SS-GEN密度在尾部渐近精确，对于正则变化分布，均匀相对误差消失；对于威布尔型分布，均匀对数相对误差消失。与现有依赖专门架构或参数尾部规范的方法不同，SS-GEN利用渐近尾部结构，使标准生成模型能够生成具有代表性的极端样本并估计超出观测数据的罕见事件概率。
英文摘要
We introduce Self-Similar Generative Estimation (SS-GEN), a method for simulating multivariate tail events and estimating rare-event probabilities in both heavy and light-tailed settings. SS-GEN exploits asymptotic tail structure to decompose the tail distribution into an explicit radial component and a nonparametric angular component, reducing tail learning to a compact-domain problem that can be handled by off-the-shelf deep generative models. The resulting sampler generates representative extreme scenarios and supports probability estimation far beyond the observed data. Under mild nonparametric tail assumptions, we show that the SS-GEN density is asymptotically exact in the tail, with vanishing uniform relative error for regularly varying distributions and vanishing uniform log-relative error for Weibull-type distributions. Unlike existing approaches that rely on specialized architectures or parametric tail specifications, SS-GEN leverages asymptotic tail structure to enable standard generative models to generate representative extreme samples and estimate rare-event probabilities beyond the observed data.
