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GMCM: Unsupervised Clustering and Meta-Analysis Using Gaussian Mixture Copula Models

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  • Bilgrau, Anders Ellern
  • Eriksen, Poul Svante
  • Rasmussen, Jakob Gulddahl
  • Johnsen, Hans Erik
  • Dybkaer, Karen
  • Boegsted, Martin

Abstract

Methods for clustering in unsupervised learning are an important part of the statistical toolbox in numerous scientific disciplines. Tewari, Giering, and Raghunathan (2011) proposed to use so-called Gaussian mixture copula models (GMCM) for general unsupervised learning based on clustering. Li, Brown, Huang, and Bickel (2011) independently discussed a special case of these GMCMs as a novel approach to meta-analysis in highdimensional settings. GMCMs have attractive properties which make them highly flexible and therefore interesting alternatives to other well-established methods. However, parameter estimation is hard because of intrinsic identifiability issues and intractable likelihood functions. Both aforementioned papers discuss similar expectation-maximization-like algorithms as their pseudo maximum likelihood estimation procedure. We present and discuss an improved implementation in R of both classes of GMCMs along with various alternative optimization routines to the EM algorithm. The software is freely available in the R package GMCM. The implementation is fast, general, and optimized for very large numbers of observations. We demonstrate the use of package GMCM through different applications.

Suggested Citation

  • Bilgrau, Anders Ellern & Eriksen, Poul Svante & Rasmussen, Jakob Gulddahl & Johnsen, Hans Erik & Dybkaer, Karen & Boegsted, Martin, 2016. "GMCM: Unsupervised Clustering and Meta-Analysis Using Gaussian Mixture Copula Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i02).
    • Handle: RePEc:jss:jstsof:v:070:i02
    DOI: http://hdl.handle.net/10.18637/jss.v070.i02
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    References listed on IDEAS

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    1. Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
    2. Smyth Gordon K, 2004. "Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-28, February.
    3. Efron, Bradley, 2004. "Large-Scale Simultaneous Hypothesis Testing: The Choice of a Null Hypothesis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 96-104, January.
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    Cited by:

    1. Sabyasachi Guharay & KC Chang & Jie Xu, 2017. "Robust Estimation of Value-at-Risk through Distribution-Free and Parametric Approaches Using the Joint Severity and Frequency Model: Applications in Financial, Actuarial, and Natural Calamities Domain," Risks, MDPI, vol. 5(3), pages 1-30, July.
    2. Fritzsch, Simon & Timphus, Maike & Weiß, Gregor, 2024. "Marginals versus copulas: Which account for more model risk in multivariate risk forecasting?," Journal of Banking & Finance, Elsevier, vol. 158(C).
    3. Kasa, Siva Rajesh & Rajan, Vaibhav, 2022. "Improved Inference of Gaussian Mixture Copula Model for Clustering and Reproducibility Analysis using Automatic Differentiation," Econometrics and Statistics, Elsevier, vol. 22(C), pages 67-97.
    4. Simon Fritzsch & Maike Timphus & Gregor Weiss, 2021. "Marginals Versus Copulas: Which Account For More Model Risk In Multivariate Risk Forecasting?," Papers 2109.10946, arXiv.org.

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