Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
156 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Support Testing in the Huge Object Model (2308.15988v3)

Published 30 Aug 2023 in cs.DS

Abstract: The Huge Object model is a distribution testing model in which we are given access to independent samples from an unknown distribution over the set of strings ${0,1}n$, but are only allowed to query a few bits from the samples. We investigate the problem of testing whether a distribution is supported on $m$ elements in this model. It turns out that the behavior of this property is surprisingly intricate, especially when also considering the question of adaptivity. We prove lower and upper bounds for both adaptive and non-adaptive algorithms in the one-sided and two-sided error regime. Our bounds are tight when $m$ is fixed to a constant (and the distance parameter $\varepsilon$ is the only variable). For the general case, our bounds are at most $O(\log m)$ apart. In particular, our results show a surprising $O(\log \varepsilon{-1})$ gap between the number of queries required for non-adaptive testing as compared to adaptive testing. For one sided error testing, we also show that a $O(\log m)$ gap between the number of samples and the number of queries is necessary. Our results utilize a wide variety of combinatorial and probabilistic methods.

Citations (3)

Summary

We haven't generated a summary for this paper yet.