Testing Poisson Binomial Distributions (original) (raw)
2014, Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms
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 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. * Supported by grant from MITEI-Shell program. † Supported by a Sloan Foundation Fellowship, a Microsoft Research Faculty Fellowship and NSF Award CCF-0953960 (CAREER) and CCF-1101491. 1 Effective support is the smallest set of contiguous integers where the distribution places all but of its probability mass.
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