A Chasm Between Identity and Equivalence Testing with Conditional Queries

A recent model for property testing of probability distributions [CFGM13, CRS15] enables tremendous savings in the sample complexity of testing algorithms, by allowing them to condition the sampling on subsets of the domain. In particular, Canonne, Ron, and Servedio [CRS15] showed that, in this setting, testing identity of an unknown distribution D (i.e., whether D = D∗ for an explicitly known D∗ ) can be done with a constant number of samples, independent of the support size n – in contrast to the required √ n in the standard sampling model. However, it was unclear whether the same held for the case of testing equivalence, where both distributions are unknown. Indeed, while Canonne, Ron, and Servedio [CRS15] established a polylog(n)-query upper bound for equivalence testing, very recently brought down to ˜O(log log n) by Falahatgar et al. [FJO+ 15], whether a dependence on the domain size n is necessary was still open, and explicitly posed by Fischer at the Bertinoro Worksho...

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Jayadev Acharya, Clément L. Canonne, Gautam Kamath
• Keywords: Algorithms, APPROX 2015