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Outlier detection in contingency tables using decomposable graphical models

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Listed:
  • Mads Lindskou
  • Poul Svante Eriksen
  • Torben Tvedebrink

Abstract

For high‐dimensional data, it is a tedious task to determine anomalies such as outliers. We present a novel outlier detection method for high‐dimensional contingency tables. We use the class of decomposable graphical models to model the relationship among the variables of interest, which can be depicted by an undirected graph called the interaction graph. Given an interaction graph, we derive a closed‐form expression of the likelihood ratio test (LRT) statistic and an exact distribution for efficient simulation of the test statistic. An observation is declared an outlier if it deviates significantly from the approximated distribution of the test statistic under the null hypothesis. We demonstrate the use of the LRT outlier detection framework on genetic data modeled by Chow–Liu trees.

Suggested Citation

  • Mads Lindskou & Poul Svante Eriksen & Torben Tvedebrink, 2020. "Outlier detection in contingency tables using decomposable graphical models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 347-360, June.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:2:p:347-360
    DOI: 10.1111/sjos.12407
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    References listed on IDEAS

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    1. Tvedebrink, Torben & Eriksen, Poul Svante & Mogensen, Helle Smidt & Morling, Niels, 2018. "Weight of the evidence of genetic investigations of ancestry informative markers," Theoretical Population Biology, Elsevier, vol. 120(C), pages 1-10.
    2. Sonja Kuhnt, 2004. "Outlier Identification Procedures for Contingency Tables using Maximum Likelihood and L1 Estimates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 431-442, September.
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