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Distribution Testing in the Presence of Arbitrarily Dominant Noise with Verification Queries
Hadley Black, Christopher Ye
https://arxiv.org/abs/2509.17269 https://

Distribution Testing in the Presence of Arbitrarily Dominant Noise with Verification Queries
We study distribution testing without direct access to a source of relevant data, but rather to one where only a tiny fraction is relevant. To enable this, we introduce the following verification query model. The goal is to perform a statistical task on distribution $\boldsymbol{p}$ given sample access to a mixture $\boldsymbol{r} = λ\boldsymbol{p} + (1-λ)\boldsymbol{q}$ and the ability to query whether a sample was generated by $\boldsymbol{p}$ or by $\boldsymbol{q}$. In general, if $m_0$ sa…