Skip to main content
SpringerLink
Log in

Exact Sublinear Binomial Sampling

  • Conference paper
Algorithms and Computation (ISAAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8283))

Included in the following conference series:

Abstract

Drawing a random variate from a given binomial distribution B(n,p) is an important subroutine in many large-scale simulations. The naive algorithm takes \(\mathcal{O}(n)\) time and has no precision loss, however, this method is often too slow in many settings. The problem of sampling from a binomial distribution in sublinear time has been extensively studied and implemented in such packages as R [22] and the GNU Scientific Library (GSL) [10], however, all known sublinear-time algorithms involve precisions loss, which introduces artifacts into the sampling, such as discontinuities.

In this paper, we present the first algorithm, to the best of our knowledge, that samples binomial distributions in sublinear time with no precision loss.

This research was supported by NSF Grants IIS-1247750 and CCF-1114930.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abe, J., Kamimura, Y.: Do female parasitoid wasps recognize and adjust sex ratios to build cooperative relationships? Journal of Evolutionary Biology 25(7), 1427–1437 (2012)

    Article  Google Scholar 

  2. Ahrens, J.H., Dieter, U.: Sampling from binomial and poisson distributions: A method with bounded computation times. Computing 25(3), 193–208 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  3. Batagelj, V., Brandes, U.: Efficient generation of large random networks. Physical Review E 71(3), 36113 (2005)

    Article  Google Scholar 

  4. Blanca, A., Mihail, M.: Efficient generation - close to G(n,p) and generalizations. CoRR abs/1204.5834 (2012)

    Google Scholar 

  5. Bringmann, K., Friedrich, T.: Exact and efficient generation of geometric random variates and random graphs. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part I. LNCS, vol. 7965, pp. 267–278. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  6. Devroye, L.: Generating the maximum of independent identically distributed random variables. Computers and Mathematics with Applications 6(3), 305–315 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  7. Devroye, L.: Non-Uniform Random Variate Generation. Springer (1986)

    Google Scholar 

  8. Feller, W.: An Introduction to Probability Theory and Its Applications, vol. 1. Wiley (January 1968)

    Google Scholar 

  9. Fox, J., Weisberg, S.: An R Companion to Applied Regression. SAGE Publications (2010)

    Google Scholar 

  10. Galassi, M., et al.: Gnu Scientific Library: Reference Manual. Network Theory Ltd. (2003)

    Google Scholar 

  11. Granlund, T.: The GMP development team: GNU MP: The GNU Multiple Precision Arithmetic Library, 5.0.5 edn. (2012), http://gmplib.org/

  12. Hörmann, W.: The generation of binomial random variates. Journal of Statistical Computation and Simulation 46, 101–110 (1993)

    Article  MATH  Google Scholar 

  13. Hörmann, W., Leydold, J., Derflinger, G.: Automatic nonuniform random variate generation. Springer (2004)

    Google Scholar 

  14. Kachitvichyanukul, V., Schmeiser, B.W.: Binomial random variate generation. Commun. ACM 31, 216–222 (1988)

    Article  MathSciNet  Google Scholar 

  15. Karney, C.F.F.: Sampling exactly from the normal distribution. CoRR abs/1303.6257 (2013)

    Google Scholar 

  16. Knuth, D., Yao, A.: The complexity of nonuniform random number generation. In: Algorithms and Complexity: New Directions and Recent Results. Academic Press (1976)

    Google Scholar 

  17. Knuth, D.E.: The art of computer programming. Seminumerical algorithms, vol. 2. Addison-Wesley Longman Publishing Co., Inc. (1997)

    Google Scholar 

  18. Kronmal, R.A., Peterson, A.V.J.: On the alias method for generating random variables from a discrete distribution. The American Statistician 33(4), 214–218 (1979)

    MathSciNet  MATH  Google Scholar 

  19. Miller, J.C., Hagberg, A.: Efficient generation of networks with given expected degrees. In: Frieze, A., Horn, P., Prałat, P. (eds.) WAW 2011. LNCS, vol. 6732, pp. 115–126. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  20. Motwani, R., Raghavan, P.: Randomized algorithms. Cambridge University Press (1995)

    Google Scholar 

  21. Patterson, R.S.: of Louisville, U.: Testing the Effects of Predictors Using Data Generated by Non-identity Link Functions of the Single-index Model: A Monte Carlo Approach. University of Louisville (2008)

    Google Scholar 

  22. R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing (2008)

    Google Scholar 

  23. Sauerhoff, M., Woelfel, P.: Time-space tradeoff lower bounds for integer multiplication and graphs of arithmetic functions. In: STOC, pp. 186–195. ACM (2003)

    Google Scholar 

  24. Serfling, R.J.: Probability Inequalities for the Sum in Sampling without Replacement. The Annals of Statistics 2(1), 39–48 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  25. Stadlober, E., Zechner, H.: The patchwork rejection technique for sampling from unimodal distributions. ACM Trans. Model. Comput. Simul. 9(1), 59–80 (1999)

    Article  Google Scholar 

  26. Stillwell, J.: Elements of Number Theory. Springer (2003)

    Google Scholar 

  27. Tsai, M.-T., Wang, D.-W., Liau, C.-J., Hsu, T.-S.: Heterogeneous subset sampling. In: Thai, M.T., Sahni, S. (eds.) COCOON 2010. LNCS, vol. 6196, pp. 500–509. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rutgers University, New Brunswick, NJ, 08901, USA

    Martín Farach-Colton & Meng-Tsung Tsai

Authors
  1. Martín Farach-Colton
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Meng-Tsung Tsai
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Chinese University of Hong Kong, Shatin, 100084, Hong Kong, China

    Leizhen Cai

  2. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Clear Water Bay, 100044, Hong Kong, China

    Siu-Wing Cheng

  3. Department of Computer Science, University of Hong Kong, Porfkulam, 100084, Hong Kong, China

    Tak-Wah Lam

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Farach-Colton, M., Tsai, MT. (2013). Exact Sublinear Binomial Sampling. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-45030-3_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45029-7

  • Online ISBN: 978-3-642-45030-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation