Description Usage Arguments Details Value Author(s) References See Also Examples
The main function for high-dimensional Mixed Graphical Models estimation.
1 |
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. |
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.
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 |
Mingyu Qi, Tianxi Li
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | 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)
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