We study distribution testing in the standard access model and the
conditional access model when the memory available to the testing algorithm is
bounded. In both scenarios, the samples appear in an online fashion and the
goal is to test the properties of distribution using an optimal number of
samples subject to a memory constraint on how many samples can be stored at a
given time. First, we provide a trade-off between the sample complexity and the
space complexity for testing identity when the samples are drawn according to
the conditional access oracle. We then show that we can learn a succinct
representation of a monotone distribution efficiently with a memory constraint
on the number of samples that are stored that is almost optimal. We also show
that the algorithm for monotone distributions can be extended to a larger class
of decomposable distributions.

在标准访问模型和条件访问模型中，当测试算法的内存受到限制时，我们研究分布测试。我们提供了一个样本复杂性和空间复杂性之间的权衡，用于在根据条件访问预言进行抽样时测试身份。我们还展示了我们可以有效地学习具有几乎最优的样本存储限制的单调分布的简洁表示。此外，我们还展示了单调分布的算法可以扩展到更大的可分解分布类。