揭示了何种不精确得分信息仍可实现无偏采样
The Tractability Landscape of Sampling with Inexact Scores
- 提出对不精确得分预言机的严格分类标准
- 证明弱于次高斯假设的误差均导致采样不可行
- 结论适用于多种误差模型，且与算法无关
我们为标准、性质良好的目标分布提供了一种简单而精确的刻画：在何种不精确得分预言机访问条件下，采样可实现趋于零的总变差偏差。核心结果表明，任何弱于[YW26]所用次高斯假设的误差类型，都会排除无偏采样的可计算性。该结论强化了[CCSW26]的结果，使其具有算法无关性，并适用于更广泛的误差假设。
原文摘要 · Abstract (English)
We provide a simple and tight characterization of the types of inexact score oracle access that permit sampling with vanishing total variation bias, for a standard, well-behaved target family. Our main result shows that any weaker error than the sub-Gaussian assumption used by [YW26] rules out the tractability of unbiased sampling. This strengthens the conclusion of [CCSW26] to be algorithm-agnostic, and to hold for a wider range of error assumptions.
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