# Small Contingency Tables with Large Gaps

@article{Sullivant2005SmallCT, title={Small Contingency Tables with Large Gaps}, author={Seth Sullivant}, journal={SIAM J. Discret. Math.}, year={2005}, volume={18}, pages={787-793} }

We construct examples of contingency tables on n binary random variables where the gap between the linear programming lower/upper bound and the true integer lower/upper bounds on cell entries is exponentially large. These examples provide evidence that linear programming may not be an effective heuristic for detecting disclosures when releasing margins of multiway tables.

## 15 Citations

On the occurrence of large gaps in small contingency tables

- Mathematics
- 2009

Examples of small contingency tables on binary random variables with large integer programming gaps on the lower bounds of cell entries were constructed by Sullivant. We argue here that the margins…

Cell Bounds in Two-Way Contingency Tables Based on Conditional Frequencies

- MathematicsPrivacy in Statistical Databases
- 2008

This paper derives the closed-form solutions for the linear relaxation bounds on cell counts of a two-way contingency table given observed conditional probabilities and compute the corresponding sharp integer bounds via integer programming and shows that there can be large differences in the width of these bounds.

Cell Bounds in k-way Tables Given Conditional Frequencies

- Computer Science
- 2012

This work considers bounds on cell counts for k-way tables when observed conditional probabilities and total sample size are released and compute sharp integer bounds using integer programming and demonstrates that, in some cases, they can be unacceptably narrow.

Algebraic Statistics and Contingency Table Problems: Log-Linear Models, Likelihood Estimation, and Disclosure Limitation

- Mathematics
- 2009

Contingency tables have provided a fertile ground for the growth of algebraic statistics. In this paper we briefly outline some features of this work and point to open research problems. We focus on…

Integrality Gaps of Integer Knapsack Problems

- Mathematics, Computer ScienceIPCO
- 2017

In a randomised setting, it is shown that the integrality gap of a “typical” knapsack problem is drastically smaller than the integralities gap that occurs in a worst case scenario.

Algebraic and Geometric Methods in Statistics: The generalised shuttle algorithm

- Computer Science, Mathematics
- 2009

The Generalized Shuttle Algorithm for computing integer bounds of multi-way contingency tables induced by arbitrary linear constraints on cell counts is described and illustrated how the algorithm can be used to compute exact p-values of goodness-of-fit tests in exact conditional inference.

Partial Information Releases for Confidential Contingency Table Entries: Present and Future Research Efforts

- BusinessJ. Priv. Confidentiality
- 2010

The main focus is the partial information release strategy, through which agencies can release relevant marginal and conditional information along with the sample size instead of a full contingency table.

Algebraic statistics

- MathematicsISSAC
- 2012

This tutorial will consist of a detailed study of two examples where the algebra/statistics connection has proven especially useful: in the study of phylogenetic models and in the analysis of contingency tables.

Rapid Mixing and Markov Bases

- MathematicsSIAM J. Discret. Math.
- 2016

It is shown that under a dilation of the underlying polytope, these random walks do not mix rapidly when a fixed Markov based is used, and this phenomenon does not disappear after adding more moves to the Markov basis.

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