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

more »

... he 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.