On the Power of Conditional Samples in Distribution Testing

We define and examine the power of the conditional-sampling oracle in the context of distribution-property testing. The conditional-sampling oracle for a discrete distribution $\mu$ takes as input a subset $S$ of the domain, and outputs a random sample $i\in S$ drawn according to $\mu$, conditioned on $S$ (and independently of all prior samples). The conditional-sampling oracle is a natural generalization of the ordinary sampling oracle in which $S$ always equals the whole domain.

We show that with the conditional-sampling oracle, testing uniformity, testing identity to a known distribution, and testing any label-invariant property of distributions is easier than with the ordinary sampling oracle. On the other hand, we also show that for some distribution properties the sample-complexity remains near-maximal even with conditional sampling.

One can use conditional sampling for various real life problems also (this is a joint work with Eldar Fischer, Yonatan Goldhirsh and Arie Matsliah).