@article{c188c5e101db4a2f8e15ed236262b1f5,

title = "Testing probability distributions using conditional samples",

abstract = "We study a new framework for property testing of probability distributions, by considering distribution testing algorithms that have access to a conditional sampling oracle. This is an oracle that takes as input a subset S ⊆ [N] of the domain [N] of the unknown probability distribution D and returns a draw from the conditional probability distribution D restricted to S. This new model allows considerable flexibility in the design of distribution testing algorithms; in particular, testing algorithms in this model can be adaptive. We study a wide range of natural distribution testing problems in this new framework and some of its variants, giving both upper and lower bounds on query complexity. These problems include testing whether D is the uniform distribution μ; testing whether D = D∗ for an explicitly provided D∗; testing whether two unknown distributions D1 and D2 are equivalent; and estimating the variation distance between D and the uniform distribution. At a high level, our main finding is that the new conditional sampling framework we consider is a powerful one: while all the problems mentioned above have Ω(√N) sample complexity in the standard model (and in some cases the complexity must be almost linear in N), we give poly(log N, 1/ε)-query algorithms (and in some cases poly(1/ε)-query algorithms independent of N) for all these problems in our conditional sampling setting.",

keywords = "Conditional sampling, Probability distributions, Property testing",

author = "Canonne, {Cl{\'e}ment L.} and Dana Ron and Servedio, {Rocco A.}",

note = "Publisher Copyright: {\textcopyright} 2015 Society for Industrial and Applied Mathematics.",

year = "2015",

doi = "10.1137/130945508",

language = "אנגלית",

volume = "44",

pages = "540--616",

journal = "SIAM Journal on Computing",

issn = "0097-5397",

publisher = "Society for Industrial and Applied Mathematics (SIAM)",

number = "3",

}