Minimax bounds for watermarked and masked recursive discrete distribution estimation

The paper investigates how watermarking affects recursive discrete distribution estimation when synthetic samples are mixed with real data. It establishes minimax lower bounds showing that, as the proportion of real samples approaches zero, adding watermarks cannot improve performance unless the false‑negative detection rate also vanishes. The authors further demonstrate that simple deterministic estimators achieve worst‑case losses close to these bounds and introduce a masking technique that reduces the remaining performance gap to a Jensen gap, suggesting potential for tighter bounds.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.