Approximating and testing k-histogram distributions in sub-linear time
Piotr Indyk, Reut Levi, Ronitt Rubinfeld · 2012
A discrete distribution p, over [n], is a k histogram if its probability distribution function can be represented as a piece-wise constant function with k pieces. Such a function is represented by a list of k intervals and k corresponding values. We consider the following problem: given a collection of samples from a distribution p, find a k-histogram that (approximately) minimizes the l 2 distance to the distribution p. We give time and sample efficient algorithms for this problem.