Approximating and testing k-histogram distributions in sub-linear time

• Main Authors: Indyk, Piotr (Contributor), Levi, Reut (Author), Rubinfeld, Ronitt (Contributor)
• Other Authors: Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory (Contributor), Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
• Format: Article
• Language: English
• Published: Association for Computing Machinery (ACM), 2014-05-15T18:13:10Z.
• Subjects: Article
• Online Access: Get fulltext

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 [subscript 2] distance to the distribution p. We give time and sample efficient algorithms for this problem. We further provide algorithms that distinguish distributions that have the property of being a k-histogram from distributions that are ε-far from any k-histogram in the l [subscript 1] distance and l [subscript 2] distance respectively.
David & Lucile Packard Foundation (Fellowship)
National Science Foundation (U.S.) (Grant CCF-0728645)
National Science Foundation (U.S.) (Grant 0732334)
National Science Foundation (U.S.) (Grant 0728645)