hmgm: High-dimensional Mixed Graphical Models Estimation

In hmgm: High-Dimensional Mixed Graphical Models Estimation

Description

The main function for high-dimensional Mixed Graphical Models estimation.

Usage

hmgm(z,y,tune1,tune2,method,kappa,penalty1=NULL,penalty2=NULL)

Arguments

z	z is a n x q discrete data matrix (n is the sample size and q is the number of discrete variables).
y	y is a n x p continous data matrix (n is the sample size and p is the number of continous variables).
tune1	Tuning parameter vector for logistic regression (rho in the orginal paper).
tune2	Tuning parameter vector for linear regression (chi in the orginal paper).
method	Can only be max or min, which implies the function takes the maximum or minimum of absolute values as the final estimate.
kappa	tuning parameters for lambda.
penalty1	Penalty for logistics regression. The default penalty is weighted lasso penalty. See details at formulation (10) in High-dimensional Mixed Graphical Models.
penalty2	Penalty for linear regression. The default penalty is weighted lasso penalty. See details atformulation (11) in High-dimensional Mixed Graphical Models.

Details

The graph structure is estimated by maximizing the conditional likelihood of one variable given the rest. We focus on the conditional log-likelihood of each variable and fit separate regressions to estimate the parameters, much in the spirit of the neighborhood selection approach proposed by Meinshausen-Buhlmann for the Gaussian graphical model and by Ravikumar for the Ising model. We incorporating a group lasso penalty, approximated by a weighted lasso penalty for computational efficiency.

Value

The function returns is a structure of fitted parameters path, the notations are the same as the paper.

fitlist_post	the fitted parameter path by taking the maximum or minimum absolute values with signs
fitlist	The original fitlist

Author(s)

Mingyu Qi, Tianxi Li

References

Jie Cheng, Tianxi Li, Elizaveta Levina, and Ji Zhu.(2017) High-dimensional Mixed Graphical Models. Journal of Computational and Graphical Statistics 26.2: 367-378, https://arxiv.org/pdf/1304.2810.pdf
Simon, N., Friedman, J., Hastie,T., Tibshirani, R. (2011) Regularization Paths for Cox's ProportionalHazards Model via Coordinate Descent, Journal of Statistical Software, Vol.39(5) 1-13, https://www.jstatsoft.org/v39/i05/
Meinshausen, N. and Buhlmann, P. (2006) High dimensional graphs and variable selection with the lasso, Annals of Statistics, 34, 1436–1462., https://arxiv.org/pdf/math/0608017.pdf
Ravikumar, P., Wainwright, M., and Lafferty, J. (2010) High-dimensionalIsing model selection using l1-regularized logistic regression,Annals of Statistics, 38, 1287–1319., https://arxiv.org/pdf/1010.0311.pdf
Liu, H., Han, F., Yuan, M., Lafferty, J., and Wasserman, L. (2012) High dimensional semiparametric Gaussian copula graphical models, Annals of Statistics, 40, 2293–2326., https://arxiv.org/pdf/1202.2169.pdf
Zhao, P., Rocha, G., and Yu, B. (2009) The composite absolute penalties family for grouped and hierarchical variable selection, The Annals of Statistics, 3468–3497., https://arxiv.org/pdf/0909.0411.pdf

See Also

datagen

Examples

n = 100
p = 20
q = 10
a = 1
b=  2
c = 1


adj = matrix(0, p+q, p+q)
adj[10:16, 10:16] = 1
adj[1:5, 1:5] = 1
adj[25:30, 25:30] = 1
adj = adj-diag(diag(adj))

parlist = pargen(adj, p, q, a, b,c)

mydata = datagen(parlist, n)

z = mydata$z

y = mydata$y

tune1 = tune2 = 0.1

kappa = 0.1

## parameter estimation

fit = hmgm(z, y, tune1, tune2, 'max', kappa)

hmgm documentation built on Jan. 13, 2021, 5:19 p.m.