Algorithms – ESA 2006

Volume 4168 of the series Lecture Notes in Computer Science pp 136-147

Negative Examples for Sequential Importance Sampling of Binary Contingency Tables

  • Ivona BezákováAffiliated withLancaster UniversityDepartment of Computer Science, University of Chicago
  • , Alistair SinclairAffiliated withLancaster UniversityComputer Science Division, University of California
  • , Daniel ŠtefankovičAffiliated withCarnegie Mellon UniversityDepartment of Computer Science, University of Rochester
  • , Eric VigodaAffiliated withCarnegie Mellon UniversityGeorgia Institute of Technology, College of Computing

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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.