Sampling streaming data with replacement

Authors:
Byung-Hoon Park;George Ostrouchov;Nagiza F. Samatova
Affiliations:
Computer Science and Mathematics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6367, USA;Computer Science and Mathematics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6367, USA;Computer Science and Mathematics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6367, USA
Venue:
Computational Statistics & Data Analysis
Year:
2007

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Abstract

Simple random sampling is a widely accepted basis for estimation from a population. When data come as a stream, the total population size continuously grows and only one pass through the data is possible. Reservoir sampling is a method of maintaining a fixed size random sample from streaming data. Reservoir sampling without replacement has been extensively studied and several algorithms with sub-linear time complexity exist. Although reservoir sampling with replacement is previously mentioned by some authors, it has been studied very little and only linear algorithms exist. A with-replacement reservoir sampling algorithm of sub-linear time complexity is introduced. A thorough complexity analysis of several approaches to the with-replacement reservoir sampling problem is also provided.