| GGMncv-package {GGMncv} | R Documentation |
GGMncv: Gaussian Graphical Models with Nonconvex Regularization
Description
The primary goal of GGMncv is to provide non-convex penalties for estimating Gaussian graphical models. These are known to overcome the various limitations of lasso (least absolute shrinkage "screening" operator), including inconsistent model selection (Zhao and Yu 2006), biased estimates (Zhang 2010), and a high false positive rate (see for example Williams and Rast 2020;Williams et al. 2019)
Several of the penalties are (continuous) approximations to the \(\ell_0\) penalty, that is, best subset selection. However, the solution does not require enumerating all possible models which results in a computationally efficient solution.
L0 Approximations
Atan:
penalty = "atan"(Wang and Zhu 2016). This is currently the default.Seamless \(\ell_0\):
penalty = "selo"(Dicker et al. 2013).Exponential:
penalty = "exp"(Wang et al. 2018)Log:
penalty = "log"(Mazumder et al. 2011).Sica:
penalty = "sica"(Lv and Fan 2009)
Additional penalties:
SCAD:
penalty = "scad"(Fan and Li 2001).MCP:
penalty = "mcp"(Zhang 2010).Adaptive lasso:
penalty = "adapt"(Zou 2006).Lasso:
penalty = "lasso"(Tibshirani 1996).
Citing GGMncv
It is important to note that GGMncv merely provides a software implementation
of other researchers work. There are no methodological innovations,
although this is the most comprehensive R package for estimating GGMs
with non-convex penalties. Hence, in addition to citing the
package citation("GGMncv"), it is important to give credit to the primary
sources. The references are provided above and in ggmncv.
Further, a survey (or review) of these penalties can be found in Williams (2020).
References
Dicker L, Huang B, Lin X (2013).
“Variable selection and estimation with the seamless-L 0 penalty.”
Statistica Sinica, 929–962.
Fan J, Li R (2001).
“Variable selection via nonconcave penalized likelihood and its oracle properties.”
Journal of the American statistical Association, 96(456), 1348–1360.
Lv J, Fan Y (2009).
“A unified approach to model selection and sparse recovery using regularized least squares.”
The Annals of Statistics, 37(6A), 3498–3528.
Mazumder R, Friedman JH, Hastie T (2011).
“Sparsenet: Coordinate descent with nonconvex penalties.”
Journal of the American Statistical Association, 106(495), 1125–1138.
Tibshirani R (1996).
“Regression shrinkage and selection via the lasso.”
Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267–288.
Wang Y, Fan Q, Zhu L (2018).
“Variable selection and estimation using a continuous approximation to the L0 penalty.”
Annals of the Institute of Statistical Mathematics, 70(1), 191–214.
Wang Y, Zhu L (2016).
“Variable selection and parameter estimation with the Atan regularization method.”
Journal of Probability and Statistics.
Williams DR (2020).
“Beyond Lasso: A Survey of Nonconvex Regularization in Gaussian Graphical Models.”
PsyArXiv.
Williams DR, Rast P (2020).
“Back to the basics: Rethinking partial correlation network methodology.”
British Journal of Mathematical and Statistical Psychology, 73(2), 187–212.
Williams DR, Rhemtulla M, Wysocki AC, Rast P (2019).
“On nonregularized estimation of psychological networks.”
Multivariate behavioral research, 54(5), 719–750.
Zhang C (2010).
“Nearly unbiased variable selection under minimax concave penalty.”
The Annals of statistics, 38(2), 894–942.
Zhao P, Yu B (2006).
“On model selection consistency of Lasso.”
Journal of Machine learning research, 7(Nov), 2541–2563.
Zou H (2006).
“The adaptive lasso and its oracle properties.”
Journal of the American statistical association, 101(476), 1418–1429.