发表机构
School of Computer and Communication Sciences, EPFL（EPFL计算机与通信科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探究带水印的递归离散分布估计的极小极大损失，提出掩码缩小损失差距，推测更严格下界可消除剩余差距。
AI 中文摘要
水印已被提出作为一种在无元数据区分合成样本与真实样本的估计场景中识别合成样本的方法，但其精确效果仍未被探究。在缺乏区分机制的情况下，已有研究表明添加合成样本会显著降低新真实样本的边际效用。本研究针对存在水印时的递归离散分布估计，对比无辅助和先知辅助的损失，研究其极小极大损失。当真实样本的比例渐近消失时，我们提供的下界表明，除非检测的假阴性率也渐近消失，否则无法通过添加水印提升性能。此外，我们证明在大多数 regime（区域）中，一系列简单确定性估计器的最坏情况损失与对应下界仅相差常数因子。最后，我们提出掩码（一种随机化过程），将剩余 regime 中的差距缩小到 Jensen 差距。我们推测更严格的下界论证可消除该差距。
英文摘要
Watermarking has been proposed as a way to identify synthetic samples in estimation settings where no metadata is available to distinguish them from real samples, but its precise effects remain unexplored. In the absence of a distinguishing mechanism, it has been shown that adding synthetic samples significantly reduces the marginal efficacy of new real samples. In this work, we study the minimax loss of such recursive discrete distribution estimation in the presence of watermarks in contrast to the unassisted and oracle-assisted losses. When the fraction of real samples vanishes asymptotically, we provide a lower bound that shows that it is impossible to improve performance by adding watermarks unless the false negative rate of detection also vanishes. Additionally, we show that in most regimes, the worst-case losses of a sequence of simple deterministic estimators match the corresponding lower bounds up to constants. Finally, we propose masking, a randomization procedure that narrows the gap in the remaining regimes to a Jensen gap. We conjecture that a tighter lower bound argument can close this gap.
CommentsShorter version to be published at the IEEE Information Theory Workshop 2026
