2012
DOI: 10.1214/12-aos1037
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High-dimensional semiparametric Gaussian copula graphical models

Abstract: We propose a semiparametric approach called the nonparanormal skeptic for efficiently and robustly estimating high dimensional undirected graphical models. To achieve modeling flexibility, we consider the nonparanormal graphical models proposed by Liu, Lafferty and Wasserman (2009). To achieve estimation robustness, we exploit nonparametric rank-based correlation coefficient estimators, including the Spearman's rho and Kendall's tau. We prove that the nonparanormal skeptic achieves the optimal parametric rates… Show more

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Cited by 445 publications
(475 citation statements)
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“…Γ 0 is called latent generalized correlation matrix (Han and Liu, 2014). Moreover, Liu et al (2009Liu et al ( , 2012 and Han and Liu (2014) Liu (2014Liu ( , 2017 developed their scale-invariant PCA based on the robust estimate of Γ 0 .…”
Section: In the Traditional Case Of Vector-valued Variablementioning
confidence: 99%
See 3 more Smart Citations
“…Γ 0 is called latent generalized correlation matrix (Han and Liu, 2014). Moreover, Liu et al (2009Liu et al ( , 2012 and Han and Liu (2014) Liu (2014Liu ( , 2017 developed their scale-invariant PCA based on the robust estimate of Γ 0 .…”
Section: In the Traditional Case Of Vector-valued Variablementioning
confidence: 99%
“…For vector-valued variables, there are some works estimating the correlation matrix based on nonparanormal distribution and Kendall's τ correlation (e.g. Liu et al, 2012;Liu, 2014, 2017;Wegkamp et al, 2016). Although Kendall's τ correlation is used in both these estimators and our proposal, there are two significant differences.…”
Section: In the Traditional Case Of Vector-valued Variablementioning
confidence: 99%
See 2 more Smart Citations
“…To do this, we formulate the problem as a text regression task, and use a Gaussian copula with probability integral transform to model the uniform marginals and their dependencies. Copula models (Schweizer and Sklar, 1983;Nelsen, 1999) are often used by statisticians (Genest and Favre, 2007;Masarotto and Varin, 2012) and economists (Chen and Fan, 2006) to study the bivariate and multivariate stochastic dependency among random variables, but they are very new to the machine learning (Ghahramani et al, 2012;Han et al, 2012;Xiang and Neville, 2013;Lopezpaz et al, 2013) and related communities (Eickhoff et al, 2013). To the best of our knowledge, even though the term "copula" is named for the resemblance to grammatical copulas in linguistics, copula models have not been explored in the NLP community.…”
Section: Introductionmentioning
confidence: 99%