Negative Examples for Sequential Importance Sampling of Binary Contingency Tables

TL;DR

This paper demonstrates that the sequential importance sampling algorithm can significantly underestimate the count of binary contingency tables in certain cases, highlighting limitations in its efficiency.

Contribution

It provides the first theoretical analysis showing SIS's potential failure in estimating binary contingency tables, and identifies conditions where it remains effective.

Findings

SIS underestimates table counts exponentially in some cases.

SIS is efficient for regular row and column sums.

First theoretical results on SIS efficiency for contingency tables.

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 the class of inputs for which SIS is effective.