Problem
Research questions and friction points this paper is trying to address.
watermarking
recursive discrete distribution estimation
false negative rate
minimax loss
masking
Minimax bounds for watermarked and masked recursive discrete distribution estimation
🤖 AI Summary
研究了在无元数据区分真实与合成样本时，通过添加水印对递归离散分布估计的影响，并提出了一种随机化方法来缩小性能差距。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
watermarking
minimax loss
masking
recursive discrete distribution estimation
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