AI 中文总结
该文在广播模型中研究二元分布测试的信息复杂度，确定三类参数区域的最优协议，推导下界与通用界，还将结果应用于集合不交性等问题的下界增强。
AI 中文摘要
我们在广播（或共享黑板）模型中研究$\text{Ber}(\boldsymbol{\beta})$与$\text{Ber}(\boldsymbol{\beta})$的分布式测试。对于具有常优势的协议，我们对每一对满足$\boldsymbol{\beta}<\boldsymbol{\beta}$的情况，在任一假设下将信息复杂度刻画至通用常数因子范围内。该刻画表明两种信息成本可能存在显著差异，并确定了三个参数区域，对应的最优协议分别基于干净样本、噪声二元对称信道及非对称Z信道。下界依赖于一种新颖的混合赫尔格-詹森-香农不等式，该不等式或具有独立研究价值。我们还通过信道上的优化问题刻画了测试任意离散分布的常优势信息复杂度，并证明二元输出信道已足够。我们得到了有界似然比分布的界，并给出了以$\boldsymbol{\beta}$散度表示的一般上界。作为应用，我们恢复了广播模型下集合不交性的下界，并针对先前工作中考虑的某些问题，在多趟流设置中推导出更强的下界。
英文摘要
We study distributed testing of $\mathrm{Ber}(α)$ versus $\mathrm{Ber}(β)$ in the broadcast, or shared-blackboard, model. For protocols with constant advantage, we characterise up to universal constant factors the information complexity under either hypothesis for every pair $β<α$. The characterisation shows that the two information costs can be quite different and identifies three parameter regimes, with optimal protocols based respectively on clean samples, a noisy binary symmetric channel, and an asymmetric $Z$-channel. The lower bounds rely on a novel mixed Hellinger--Jensen--Shannon inequality that may be of independent interest. We also characterise the constant-advantage information complexity of testing arbitrary discrete distributions via an optimisation problem over channels, and show that binary-output channels suffice. We obtain bounds for bounded likelihood-ratio distributions, and give general upper bounds in terms of $χ^2$ divergence. As applications, we recover the broadcast-model set-disjointness lower bound, and derive stronger lower bounds in the multi-pass streaming setting for some problems considered in prior work.
