Conditional inference given partial information in contingency tables using Markov bases

Karwa, Vishesh; Slavković, Aleksandra

doi:10.1002/wics.1256

Cited by 7 publications

(8 citation statements)

References 53 publications

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“…If the obtained level of explanatory correlationt 1 is easily predictable from the existing informationt 0 andt 2 , it should not be regarded as statistically significant. In exact logistic regression, the sample space is defined as the set of all class vectors whose positive class size and covariate correlation are constrained to the observed value, called a fiber [16],…”

Section: Exact Logistic Regressionmentioning

confidence: 99%

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Privacy-Preserving Statistical Analysis by Exact Logistic Regression

duVerle

Kawasaki

Yamada

et al. 2015

2015 IEEE Security and Privacy Workshops

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Logistic regression is the method of choice in most genome-wide association studies (GWAS). Due to the heavy cost of performing iterative parameter updates when training such a model, existing methods have prohibitive communication and computational complexities that make them unpractical for reallife usage.We propose a new sampling-based secure protocol to compute exact statistics, that requires a constant number of communication rounds and a much lower number of computations. The publicly available implementation of our protocol (and its many optional optimisations adapted to different security scenarios) can, in a matter of hours, perform statistical testing of over 600 SNP variables across thousands of patients while accounting for potential confounding factors in the clinical data. IEEE CS Security and Privacy Workshops

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Section: Exact Logistic Regressionmentioning

confidence: 99%

“…Nevertheless, it can be achieved using Markov chain Monte Carlo methods [16], [15], [17]. It is also possible to use continuous variables [18].…”

Section: Exact Logistic Regressionmentioning

confidence: 99%

Privacy-Preserving Statistical Analysis by Exact Logistic Regression

duVerle

Kawasaki

Yamada

et al. 2015

2015 IEEE Security and Privacy Workshops

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“…In summary, their paper has the same starting point as ours and is aimed at addressing the problem structure, but they take a very different approach and focus on topics complementing those treated here. Karwa and Slavković [16] use similar methods to address conditional inference in contingency tables.…”

Section: Related and Ongoing Workmentioning

confidence: 99%

An Intuitive Formulation and Solution of the Exact Cell-Bounding Problem for Contingency Tables of Conditional Frequencies

Wright

Smucker

2014

JPC

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Recent research has raised questions about the structure and calculation of bounds on the underlying cell counts for a contingency table released in the form of conditional probabilities. This problem has implications for statistical disclosure limitation. We elucidate the mathematical structure of the problem in fairly elementary terms, under the assumption that the unrounded conditionals and sample size are known. To do so, we reformulate a standard integer programming approach as a knapsack problem, show that this provides many insights into the problem, and provide illustrations in the context of several datasets. In particular, we demonstrate that the tightest bounds are much easier to calculate than previously believed, and we also identify circumstances in which disclosure is either guaranteed or unlikely to occur.

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“…There are also tools, often based in algebraic statistics, to sample conditional distributions preserving certain statistics for contingency tables. Karwa and Slavkovic [2013] give a survey of Markov Chain Monte Carlo (MCMC) techniques to sample conditional distributions. Another approach is sequential importance sampling, proposed by Chen et al [2006].…”

Section: Introductionmentioning

confidence: 99%

One Step to Efficient Synthetic Data

Awan

Cai

2020

Preprint

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We propose a general method of producing synthetic data, which is widely applicable for parametric models, has asymptotically efficient summary statistics, and is both easily implemented and highly computationally efficient. Our approach allows for the construction of both partially synthetic datasets, which preserve the summary statistics without formal privacy methods, as well as fully synthetic data which satisfy the strong guarantee of differential privacy (DP), both with asymptotically efficient summary statistics. While our theory deals with asymptotics, we demonstrate through simulations that our approach offers high utility in small samples as well. In particular we 1) apply our method to the Burr distribution, evaluating the parameter estimates as well as distributional properties with the Kolmogorov-Smirnov test, 2) demonstrate the performance of our mechanism on a log-linear model based on a car accident dataset, and 3) produce DP synthetic data for the beta distribution using a customized Laplace mechanism.Preprint. Under review.

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Conditional inference given partial information in contingency tables using Markov bases

Cited by 7 publications

References 53 publications

Privacy-Preserving Statistical Analysis by Exact Logistic Regression

Privacy-Preserving Statistical Analysis by Exact Logistic Regression

An Intuitive Formulation and Solution of the Exact Cell-Bounding Problem for Contingency Tables of Conditional Frequencies

One Step to Efficient Synthetic Data

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