The joint graphical lasso for inverse covariance estimation across multiple classes

By Peter J. Danaher, Pei Wang, Daniela M. Witten. Journal of The Royal Statistical Society Series B-statistical Methodology, 2011

922 citations recorded by the source corpus.

We consider the problem of estimating multiple related Gaussian graphical models from a high dimensional data set with observations belonging to distinct classes. We propose the joint graphical lasso, which borrows strength across the classes to estimate multiple graphical models that share certain characteristics, such as the locations or weights of non‐zero edges. Our approach is based on maximizing a penalized log‐likelihood. We employ generalized fused lasso or group lasso penalties and implement a fast alternating directions method of multipliers algorithm to solve the corresponding convex optimization problems. The performance of the method proposed is illustrated through simulated and real data examples.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e4f8536b067127e5269316832a4733def51c399a

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In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Global Testing and Large-Scale Multiple Testing for High-Dimensional Covariance Structures (2017, background): “…inference for a given Gaussian graph, it is of significant interest in many applications to understand whether and how the network changes between disease states (de la Fuente 2010; Ideker and Krogan 2012; Hudson et al. 2009; Li et al. 2007; Danaher et al. 2014; Zhao et al. 2014; Xia et al. 2015).”
CoinFold: a web server for protein contact prediction and contact-assisted protein folding (2016, methodology): “We estimate the K precision matrices by taking into account their correlation using Group Graphical Lasso (GGL) (11) as follows. max Ω log likelihood − λ1 ∑K k=1 ∥∥Ωk ∥∥ 1 − ∑G g=1 λg ∥∥ g ∥∥ 2 where the last penalty item enforces that the column pairs in the same group have similar interaction stre”
Structure Learning in Graphical Modeling (2016, methodology): “Danaher et al. (2014) propose instead the use of group or fused lasso penalties speciﬁed in terms of the inverse covariances.”
Joint estimation of multiple networks from time course data (2013, methodology): “The frequentist approaches described by Danaher et al. (2012); Guo et al. (2011); Yang et al.”
Partial Separability and Functional Graphical Models for Multivariate Gaussian Processes (2019, methodology): “Although the joint graphical lasso estimator in [8] was proposed for borrowing structural information across multiple classes of multivariate data, it is utilized here for a slightly different purpose.”
Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data (2017, methodology): “This optimization problem has a known analytical solution [10],”
Stability and variability of personality networks. A tutorial on recent developments in network psychometrics (2017, methodology): “This technique has not been implemented yet for FGL, but the analysis performed on the entire sample provides a proxy of the stability of the results also for the FGL.”