Joint estimation of multiple high-dimensional Gaussian copula graphical models

2017 ◽  
Vol 59 (3) ◽  
pp. 289-310 ◽  
Author(s):  
Yong He ◽  
Xinsheng Zhang ◽  
Jiadong Ji ◽  
Bin Liu
Keyword(s):  
Graphical Models ◽  
Joint Estimation ◽  
Gaussian Copula ◽  
High Dimensional

scholarly journals High-dimensional joint estimation of multiple directed Gaussian graphical models

2020 ◽  
Vol 14 (1) ◽  
pp. 2439-2483
Author(s):  
Yuhao Wang ◽  
Santiago Segarra ◽  
Caroline Uhler
Keyword(s):  
Graphical Models ◽  
Joint Estimation ◽  
High Dimensional ◽  
Gaussian Graphical Models

scholarly journals High-dimensional semiparametric Gaussian copula graphical models

2012 ◽  
Vol 40 (4) ◽  
pp. 2293-2326 ◽  
Author(s):  
Han Liu ◽  
Fang Han ◽  
Ming Yuan ◽  
John Lafferty ◽  
Larry Wasserman
Keyword(s):  
Graphical Models ◽  
Gaussian Copula ◽  
High Dimensional

scholarly journals Joint estimation of multiple graphical models

Biometrika ◽  
2011 ◽  
Vol 98 (1) ◽  
pp. 1-15 ◽  
Author(s):  
J. Guo ◽  
E. Levina ◽  
G. Michailidis ◽  
J. Zhu
Keyword(s):  
Graphical Models ◽  
Joint Estimation

scholarly journals The ‘Un-Shrunk’ Partial Correlation in Gaussian Graphical Models

2020 ◽  
Author(s):  
Victor Bernal ◽  
Rainer Bischoff ◽  
Peter Horvatovich ◽  
Victor Guryev ◽  
Marco Grzegorczyk
Keyword(s):  
Graphical Models ◽  
Regulatory Networks ◽  
Partial Correlation ◽  
High Dimensional ◽  
Dimensional Problem ◽  
Gaussian Graphical Models ◽  
High Dimensional Problem ◽  
Non Linear ◽  
Partial Correlations ◽  
Molecular Profiles

Abstract Background: In systems biology, it is important to reconstruct regulatory networks from quantitative molecular profiles. Gaussian graphical models (GGMs) are one of the most popular methods to this end. A GGM consists of nodes (representing the transcripts, metabolites or proteins) inter-connected by edges (reflecting their partial correlations). Learning the edges from quantitative molecular profiles is statistically challenging, as there are usually fewer samples than nodes (‘high dimensional problem’). Shrinkage methods address this issue by learning a regularized GGM. However, it is an open question how the shrinkage affects the final result and its interpretation.Results: We show that the shrinkage biases the partial correlation in a non-linear way. This bias does not only change the magnitudes of the partial correlations but also affects their order. Furthermore, it makes networks obtained from different experiments incomparable and hinders their biological interpretation. We propose a method, referred to as the ‘un-shrunk’ partial correlation, which corrects for this non-linear bias. Unlike traditional methods, which use a fixed shrinkage value, the new approach provides partial correlations that are closer to the actual (population) values and that are easier to interpret. We apply the ‘un-shrunk’ method to two gene expression datasets from Escherichia coli and Mus musculus.Conclusions: GGMs are popular undirected graphical models based on partial correlations. The application of GGMs to reconstruct regulatory networks is commonly performed using shrinkage to overcome the “high-dimensional” problem. Besides it advantages, we have identified that the shrinkage introduces a non-linear bias in the partial correlations. Ignoring this type of effects caused by the shrinkage can obscure the interpretation of the network, and impede the validation of earlier reported results.

scholarly journals The ‘un-shrunk’ partial correlation in Gaussian graphical models

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Victor Bernal ◽  
Rainer Bischoff ◽  
Peter Horvatovich ◽  
Victor Guryev ◽  
Marco Grzegorczyk
Keyword(s):  
Graphical Models ◽  
Regulatory Networks ◽  
Partial Correlation ◽  
High Dimensional ◽  
Dimensional Problem ◽  
Gaussian Graphical Models ◽  
High Dimensional Problem ◽  
Non Linear ◽  
Partial Correlations ◽  
Molecular Profiles

Abstract Background In systems biology, it is important to reconstruct regulatory networks from quantitative molecular profiles. Gaussian graphical models (GGMs) are one of the most popular methods to this end. A GGM consists of nodes (representing the transcripts, metabolites or proteins) inter-connected by edges (reflecting their partial correlations). Learning the edges from quantitative molecular profiles is statistically challenging, as there are usually fewer samples than nodes (‘high dimensional problem’). Shrinkage methods address this issue by learning a regularized GGM. However, it remains open to study how the shrinkage affects the final result and its interpretation. Results We show that the shrinkage biases the partial correlation in a non-linear way. This bias does not only change the magnitudes of the partial correlations but also affects their order. Furthermore, it makes networks obtained from different experiments incomparable and hinders their biological interpretation. We propose a method, referred to as ‘un-shrinking’ the partial correlation, which corrects for this non-linear bias. Unlike traditional methods, which use a fixed shrinkage value, the new approach provides partial correlations that are closer to the actual (population) values and that are easier to interpret. This is demonstrated on two gene expression datasets from Escherichia coli and Mus musculus. Conclusions GGMs are popular undirected graphical models based on partial correlations. The application of GGMs to reconstruct regulatory networks is commonly performed using shrinkage to overcome the ‘high-dimensional problem’. Besides it advantages, we have identified that the shrinkage introduces a non-linear bias in the partial correlations. Ignoring this type of effects caused by the shrinkage can obscure the interpretation of the network, and impede the validation of earlier reported results.

scholarly journals Jewel: A Novel Method for Joint Estimation of Gaussian Graphical Models

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2105
Author(s):  
Claudia Angelini ◽  
Daniela De De Canditiis ◽  
Anna Plaksienko
Keyword(s):  
Graphical Models ◽  
Regulatory Networks ◽  
Regularization Parameter ◽  
Estimation Method ◽  
Real Data ◽  
Penalized Regression ◽  
Joint Estimation ◽  
Gaussian Graphical Models ◽  
Lasso Penalty ◽  
Independence Structure

In this paper, we consider the problem of estimating multiple Gaussian Graphical Models from high-dimensional datasets. We assume that these datasets are sampled from different distributions with the same conditional independence structure, but not the same precision matrix. We propose jewel, a joint data estimation method that uses a node-wise penalized regression approach. In particular, jewel uses a group Lasso penalty to simultaneously guarantee the resulting adjacency matrix’s symmetry and the graphs’ joint learning. We solve the minimization problem using the group descend algorithm and propose two procedures for estimating the regularization parameter. Furthermore, we establish the estimator’s consistency property. Finally, we illustrate our estimator’s performance through simulated and real data examples on gene regulatory networks.

EXPRESS: Handling Endogenous Regressors using Copulas: A Generalization to Linear Panel Models with Fixed Effects and Correlated Regressors

2021 ◽  
pp. 002224372110708
Author(s):  
Rouven E. Haschka
Keyword(s):  
Fixed Effects ◽  
Estimation Method ◽  
Copula Function ◽  
Small Time ◽  
Joint Estimation ◽  
Gaussian Copula ◽  
Correlated Errors ◽  
Finite Sample ◽  
Panel Models ◽  
Endogenous Regressors

This paper proposes a panel data generalization for a recently suggested IVfree estimation method that builds on joint estimation. The author shows how the method can be extended to linear panel models by combining fixed-effects transformations with the common GLS transformation to allow for heterogeneous intercepts. To account for between-regressor dependence, the author proposes determining the joint distribution of the error term and all explanatory variables using a Gaussian copula function, with the distinction that some variables are endogenous and the others are exogenous. The identification does not require any instrumental variables if the regressor-error relation is nonlinear. With a normally distributed error, nonnormally distributed endogenous regressors are therefore required. Monte Carlo simulations assess the finite sample performance of the proposed estimator and demonstrate its superiority to conventional instrumental variable estimation. A specific advantage of the proposed method is that the estimator is unbiased in dynamic panel models with small time dimensions and serially correlated errors; therefore, it is a useful alternative to GMM-style instrumentation. The practical applicability of the proposed method is demonstrated via an empirical example.

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