研究倾斜分布采样效率，发现有界与无界变量的采样成本差异巨大。
Fundamental limits for weighted empirical approximations of tilted distributions
- 提出自归一化重要性采样在倾斜分布中的渐近效率分析方法。
- 有界变量采样数随倾斜度多项式增长，无界变量则超多项式增长。
- 适用于金融、气候科学等罕见事件模拟领域研究者参考。
考虑从未知分布的随机向量生成倾斜分布样本的问题，该问题在金融、气候科学及罕见事件模拟中具有应用价值。本文研究了自归一化重要性采样在倾斜分布中的渐近效率。我们给出了其精度的精确刻画，取决于样本数量和倾斜程度。研究发现存在显著二分：对于有界随机向量，准确倾斜所需的样本数随倾斜程度呈多项式增长；而对于无界分布，所需样本数则以超多项式速率增长。
原文摘要 · Abstract (English)
Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in rare event simulation. In this article, we discuss the asymptotic efficiency of a self-normalized importance sampler of the tilted distribution. We provide a sharp characterization of its accuracy, given the number of samples and the degree of tilt. Our findings reveal a surprising dichotomy: while the number of samples needed to accurately tilt a bounded random vector increases polynomially in the tilt amount, it increases at a super polynomial rate for unbounded distributions.
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