Testing Poisson Binomial Distributions
This addresses a statistical testing problem for researchers in theoretical computer science and statistics, offering an incremental algorithmic improvement.
The paper tackles the problem of testing whether a distribution is a Poisson Binomial distribution or far from all such distributions, providing a sample near-optimal algorithm with a sample complexity of O(n^{1/4}) and a matching lower bound, which improves quadratically over naive approaches.
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.