High Dimensional Semiparametric Gaussian Copula Graphical Models

By Han Liu, Fang Han, Ming Yuan, John D. Lafferty, Larry A. Wasserman. 2012

228 citations recorded by the source corpus.

We propose a semiparametric approach, named nonparanormal skeptic, for estimating high dimensional undirected graphical models. In terms of modeling, we consider the nonparanormal family proposed by Liu et al (2009). In terms of estimation, we exploit nonparametric rank-based correlation coefficient estimators including the Spearman's rho and Kendall's tau. In high dimensional settings, we prove that the nonparanormal skeptic achieves the optimal parametric rate of convergence in both graph and parameter estimation. This result suggests that the nonparanormal graphical models are a safe replacement of the Gaussian graphical models, even when the data are Gaussian.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Kernel‐based tests for joint independence (2016, neutral): “, 2016) or also non-parametric and semiparametric copula-based correlations (Liu et al., 2012; Xue and Zou, 2012; Wegkamp and Zhao, 2016; Gaißer et al., 2010).”
High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes (2019, methodology): “Previous work [18] has applied PCA as a preprocessing step for uncovering latent structure.”
Sufficient Forecasting Using Factor Models (2015, methodology): “For example, Forni et al. (2000, 2015) studied factor estimation based on projection, Liu et al. (2012), Xue and Zou (2012) and Fan et al. (2015b) employed rank-based methods for robust estimation of the covariance matrices, and Connor et al. (2012) applied a weighted additive nonparametric…”
Estimating psychological networks and their accuracy: A tutorial paper (2016, methodology): “For continuous data that are not normally distributed, a transformation can be applied (e.g., by using the nonparanormal transformation; Liu et al., 2012) before estimating the GGM.”
Analysis of elliptical copula correlation factor model with Kendall's tau (2013, methodology): “Inspired by this observation, both [28] and [46] employ Σ̂, a variant of Σ̂ using Spearman’s rho statistic, to study the estimation of precision matrix under this setting.”
Estimating Sparse Precision Matrix: Optimal Rates of Convergence and Adaptive Estimation (2012, background): “Several recent papers considered the estimation of nonparanormal graphical models where the population distribution is non-Gaussian, see Xue and Zou (2012) and Liu, et al. (2012).”
Challenges of Big Data Analysis (2013, unknown): “These include To handle these challenges, it is urgent to develop statisticalmethodsthatarerobusttodatacomplexity (see,forexample,[115–117]),noises[62”
Structure Learning in Graphical Modeling (2016, background): “Liu et al. (2012a) and Xue & Zou (2012) observe that eﬃcient estimation in the copula models can be based on Kendall’s τ and Spearman’s ρ .”
Regularized rank-based estimation of high-dimensional nonparanormal graphical models (2012, methodology): “A referee informed us in his/her review report that Liu et al. (2012) also independently used the rank-based correlation in the context of nonparametric Gaussian graphical model estimation.”
An Overview on the Estimation of Large Covariance and Precision Matrices (2015, unknown): “ Compared to the sample covariance matrix, a remarkable property of Rband ˙b j is that they concentrate to their population quantities exponentially fast even for heavy-tailed data. More specically, Liu et al. (2012b) show that kRb Rk max = O P r logp T and max 1jp b˙ j ˙ j = O P r logp T : (25) I”