检验聚集数据的概率分布
Testing probability distributions underlying aggregated data
摘要：
本文分析和研究了概率分布测试和学习的混合模型。这里，除了样本之外，测试算法还被提供有两种不同类型的神谕之一，用于$[n]$上的未知分布$D$。更准确地说，我们定义了双重和累积双重访问模型，其中算法$A$既可以从$D$中采样，又可以分别对任何$i\in[n]$查询概率质量$D(i)$（query access）;或-得到$\{1,\dots,i\}$的总质量，即$\sum_{j=1}^i D(j)$（累积访问）这两个模型，通过推广以前研究的抽样和查询预言模型，允许我们绕过这些设置中为许多问题建立的强下限，同时捕获这些问题的几个有趣方面-并提供对模型局限性的新见解。最后，我们表明，虽然测试算法可以在大多数情况下严格更有效，一些任务仍然很难，即使有这个额外的权力。
英文摘要：
In this paper, we analyze and study a hybrid model for testing and learning probability distributions. Here, in addition to samples, the testing algorithm is provided with one of two different types of oracles to the unknown distribution $D$ over $[n]$. More precisely, we define both the dual and cumulative dual access models, in which the algorithm $A$ can both sample from $D$ and respectively, for any $i\in[n]$, - query the probability mass $D(i)$ (query access); or - get the total mass of $\{1,\dots,i\}$, i.e. $\sum_{j=1}^i D(j)$ (cumulative access) These two models, by generalizing the previously studied sampling and query oracle models, allow us to bypass the strong lower bounds established for a number of problems in these settings, while capturing several interesting aspects of these problems -- and providing new insight on the limitations of the models. Finally, we show that while the testing algorithms can be in most cases strictly more efficient, some tasks remain hard even with this additional power.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
