Negative Examples for Sequential Importance Sampling of Binary Contingency Tables

  • Ivona Bezáková
  • Alistair Sinclair
  • Daniel Štefankovič
  • Eric Vigoda
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)

Abstract

The sequential importance sampling (SIS) algorithm has gained considerable popularity for its empirical success. One of its noted applications is to the binary contingency tables problem, an important problem in statistics, where the goal is to estimate the number of 0/1 matrices with prescribed row and column sums. We give a family of examples in which the SIS procedure, if run for any subexponential number of trials, will underestimate the number of tables by an exponential factor. This result holds for any of the usual design choices in the SIS algorithm, namely the ordering of the columns and rows. These are apparently the first theoretical results on the efficiency of the SIS algorithm for binary contingency tables. Finally, we present experimental evidence that the SIS algorithm is efficient for row and column sums that are regular. Our work is a first step in determining rigorously the class of inputs for which SIS is effective.

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References

  1. 1.
    Bezáková, I., Bhatnagar, N., Vigoda, E.: Sampling Binary Contingency Tables with a Greedy Start. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (2006)Google Scholar
  2. 2.
    Bezáková, I., Sinclair, A., Štefankovič, D., Vigoda, E.: Negative Examples for Sequential Importance Sampling of Binary Contingency Tables. Available from Mathematics arXiv math. ST/0606650 (submitted)Google Scholar
  3. 3.
    Bezáková, I., Štefankovič, D., Vazirani, V., Vigoda, E.: Accelerating Simulated Annealing for the Permanent and Combinatorial Counting Problems. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (2006)Google Scholar
  4. 4.
    Chen, Y., Diaconis, P., Holmes, S., Liu, J.S.: Sequential Monte Carlo Methods for Statistical Analysis of Tables. Journal of the American Statistical Association 100, 109–120 (2005)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    De Iorio, M., Griffiths, R.C., Lebois, R., Rousset, F.: Stepwise Mutation Likelihood Computation by Sequential Importance Sampling in Subdivided Population Models. Theor. Popul. Biol. 68, 41–53 (2005)MATHCrossRefGoogle Scholar
  6. 6.
    Jerrum, M.R., Sinclair, A., Vigoda, E.: A Polynomial-time Approximation Algorithm for the Permanent of a Matrix with Non-negative Entries. Journal of the Association for Computing Machinery 51(4), 671–697 (2004)MathSciNetMATHGoogle Scholar
  7. 7.
    Miguez, J., Djuric, P.M.: Blind Equalization by Sequential Importance Sampling. In: Proceedings of the IEEE International Symposium on Circuits and Systems, pp. 845–848 (2002)Google Scholar
  8. 8.
    Zhang, J.L., Liu, J.S.: A New Sequential Importance Sampling Method and its Application to the Two-dimensional Hydrophobic-Hydrophilic Model. J. Chem. Phys. 117, 3492–3498 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ivona Bezáková
    • 1
  • Alistair Sinclair
    • 2
  • Daniel Štefankovič
    • 3
  • Eric Vigoda
    • 4
  1. 1.Department of Computer ScienceUniversity of ChicagoChicagoUSA
  2. 2.Computer Science DivisionUniversity of CaliforniaBerkeleyUSA
  3. 3.Department of Computer ScienceUniversity of RochesterRochesterUSA
  4. 4.Georgia Institute of TechnologyCollege of ComputingAtlantaUSA

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