Testing Poisson Binomial Distributions
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Daskalakis_Testing poisson.pdf
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222.83 KB
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Adobe PDF
Checksum (MD5)
956e742517982b4b1e99062302cbd33f
Author(s)
Acharya, Jayadev
Daskalakis, Konstantinos
Date Issued
2015
Journal
Proceedings of the Twenty-sixth Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Society for Industrial and Applied Mathematics
Citation
Acharya, Jayadev, and Constantinos Daskalakis. “Testing Poisson Binomial Distributions.” Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms (December 22, 2014): 1829–1840.
Version
Original manuscript
Abstract
A Poisson Binomial distribution over n variables is the distribution of the sum of n independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution P supported on {0, …, n} to which we have sample access is a Poisson Binomial distribution, or far from all Poisson Binomial distributions. The sample complexity of our algorithm is O(n[superscript 1/4]) to which we provide a matching lower bound. We note that our sample complexity improves quadratically upon that of the naive “learn followed by tolerant-test” approach, while instance optimal identity testing [VV14] is not applicable since we are looking to simultaneously test against a whole family of distributions.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1137/1.9781611973730.122
