Testing Random Variables for Independence and Identity
نویسندگان
چکیده
Given access to independent samples of a distribution A over [n℄ [m℄, we show how to test whether the distributions formed by projecting A to each coordinate are independent, i.e., whether A is -close in the L1 norm to the product distribution A1 A2 for some distributionsA1 over [n℄ and A2 over [m℄. The sample complexity of our test is ~ O(n2=3m1=3poly( 1)), assuming without loss of generality that m n. We also give a matching lower bound, up to poly(logn; 1) factors. Furthermore, given access to samples of a distribution X over [n℄, we show how to test if X is -close in L1 norm to an explicitly specified distribution Y . Our test uses ~ O(n1=2poly( 1)) samples, which nearly matches the known tight bounds for the case when Y is uniform.
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