Complexity theory typically studies the complexity of computing a function h(x) : {0, 1}n → {0, 1}m of a given input x. We advocate the study of the complexity of generating the distribution h(x) for uniform x, given random bits. Our main results are: • There are explicit AC circuits of size poly(n) and depth O(1) whose output distribution has statistical distance 1/2n from the distribution (X,...

Abstract Improvements in technology lead to increasing availability of large data sets which makes the need for reduction and informative subsamples ever more important. In this paper we construct D -optimal subsampling designs polynomial regression one covariate invariant distributions covariate. We study quadratic closely specific distributions. particular make statements on shape resulting o...