Approximating and testing k-histogram distributions in sub-linear time
Name
Indyk_Approximating and.pdf
Size
291.6 KB
Format
Adobe PDF
Checksum (MD5)
99d5063c339cb96985069883b2d18d6b
Author(s)
Indyk, Piotr
Levi, Reut
Rubinfeld, Ronitt
Date Issued
May 2012
Journal
Proceedings of the 31st symposium on Principles of Database Systems (PODS '12)
Publisher
Association for Computing Machinery (ACM)
Citation
Piotr Indyk, Reut Levi, and Ronitt Rubinfeld. 2012. Approximating and testing k-histogram distributions in sub-linear time. In Proceedings of the 31st symposium on Principles of Database Systems (PODS '12), Markus Krötzsch (Ed.). ACM, New York, NY, USA, 15-22.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/2213556.2213561
