Testing properties of distributions in the streaming model

TL;DR

This paper investigates the problem of testing distribution properties in streaming models with limited memory, providing new trade-offs and algorithms for identity testing and distribution learning.

Contribution

It introduces a trade-off between sample and space complexity for identity testing and presents efficient algorithms for learning monotone and decomposable distributions under memory constraints.

Findings

Established a sample-space trade-off for identity testing with conditional access

Developed near-optimal algorithms for learning monotone distributions with limited memory

Extended algorithms to a broader class of decomposable distributions

Abstract

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.