European Symposium on Algorithms

ESA 2006: Algorithms – ESA 2006 pp 136-147

Negative Examples for Sequential Importance Sampling of Binary Contingency Tables

  • Ivona Bezáková
  • Alistair Sinclair
  • Daniel Štefankovič
  • Eric Vigoda
Conference paper

DOI: 10.1007/11841036_15

Volume 4168 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Bezáková I., Sinclair A., Štefankovič D., Vigoda E. (2006) Negative Examples for Sequential Importance Sampling of Binary Contingency Tables. In: Azar Y., Erlebach T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg

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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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