Resolution Limits of Non-Adaptive Querying for Noisy 20 Questions Estimation

We study fundamental limits of estimation accuracy for the noisy 20 questions problem with measurement-dependent noise and introduce optimal non-adaptive procedures that achieve these limits. The minimal achievable resolution is defined as the absolute difference between the estimated and the true v...

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Bibliographic Details
Published inProceedings / IEEE International Symposium on Information Theory pp. 2167 - 2172
Main Authors Zhou, Lin, Hero, Alfred
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.06.2020
Subjects
Accuracy
Benchmark testing
Channel coding
Channel estimation
Estimation
Lower bound
Noise
Noise measurement
Random variables
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Summary:We study fundamental limits of estimation accuracy for the noisy 20 questions problem with measurement-dependent noise and introduce optimal non-adaptive procedures that achieve these limits. The minimal achievable resolution is defined as the absolute difference between the estimated and the true values of the target random variable, given a finite number of queries constrained by the excess-resolution probability. Inspired by the relationship between the 20 questions problem and the channel coding problem, we derive non-asymptotic bounds on the minimal achievable resolution. Furthermore, applying the Berry-Esseen theorem to our non-asymptotic bounds, we obtain a second-order asymptotic approximation to finite blocklength performance, specifically the achievable resolution of optimal non-adaptive query procedures with a finite number of queries subject to the excess-resolution probability constraint.
ISSN:2157-8117
DOI:10.1109/ISIT44484.2020.9174277