Efficient Sampling Methods for Discrete Distributions

Efficient Sampling Methods for Discrete Distributions We study the fundamental problem of the exact and efficient generation of random values from a finite and discrete probability distribution. Suppose that we are given n distinct events with associated probabilities $$p_1, \dots , p_n$$ p 1 , ⋯ , p n . First, we consider the problem of sampling from the distribution where the i-th event has probability proportional to $$p_i$$ p i . Second, we study the problem of sampling a subset which includes the i-th event independently with probability $$p_i$$ p i . For both problems we present on two different classes of inputs—sorted and general probabilities—efficient data structures consisting of a preprocessing and a query algorithm. Varying the allotted preprocessing time yields a trade-off between preprocessing and query time, which we prove to be asymptotically optimal everywhere. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algorithmica Springer Journals

Efficient Sampling Methods for Discrete Distributions

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Publisher
Springer US
Copyright
Copyright © 2016 by The Author(s)
Subject
Computer Science; Algorithm Analysis and Problem Complexity; Theory of Computation; Mathematics of Computing; Algorithms; Computer Systems Organization and Communication Networks; Data Structures, Cryptology and Information Theory
ISSN
0178-4617
eISSN
1432-0541
D.O.I.
10.1007/s00453-016-0205-0
Publisher site
See Article on Publisher Site

Abstract

We study the fundamental problem of the exact and efficient generation of random values from a finite and discrete probability distribution. Suppose that we are given n distinct events with associated probabilities $$p_1, \dots , p_n$$ p 1 , ⋯ , p n . First, we consider the problem of sampling from the distribution where the i-th event has probability proportional to $$p_i$$ p i . Second, we study the problem of sampling a subset which includes the i-th event independently with probability $$p_i$$ p i . For both problems we present on two different classes of inputs—sorted and general probabilities—efficient data structures consisting of a preprocessing and a query algorithm. Varying the allotted preprocessing time yields a trade-off between preprocessing and query time, which we prove to be asymptotically optimal everywhere.

Journal

AlgorithmicaSpringer Journals

Published: Aug 29, 2016

References

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