JGL_cv: Joint Graphical Lasso with k-fold crossvalidation

In GiulioCostantini/JGL2: JGL2: Joint Graphical Lasso, select the lambda parameters using AIC or crossvalidation

Description

Fits a Joint Graphical Lasso model. The lambda 1 and lambda 2 parameters are identified through k-fold crossvalidation. The cost function for the k-fold crossvalidation procedure is the average predictive negative loglikelihood, as defined in Guo et al. (2011, p.5)

Usage

JGL_cv(dat, splt, ncand = 20, l2max = 10, seed, k = 10, ncores = 1, aicfun = AIC_jgl, ...)

Arguments

dat	A dataset that includes the variables on which the gaussian graphical models should be computed, plus an additional factor "splt" which defines different classes.
splt	Character string. The name of the variable in dat that defines different classes
ncand	Integer. number of values for lambda 1 and for lambda 2
l2max	Numeric. Maximum value of the lasso parameter lambda2
seed	seed parameter that ensures the exact reproducibility of the results obtained through the k-fold crossvalidation. If Missing the seed is not set (this is good for bootstrapping and similar things)
k	number of splits for the k-fold crossvalidation
ncores	Number of cores to use. The function is optimized for parallel computing in Windows, parallel computing may not work on other systems.
aicfun	AIC.jgl or another function that take as input (1) the output of JGL, (2) n = vector of sample sizes, (3) S = list of covariance matrices. Differnetly from JGL_AIC_sequentialsearch and from JGL_AIC_widesearch, the aicfun is not used in the choice of the parameters lambda 1 and lambda 2, it has been included here only for consistency with the other functions.
...	Other parameters for link{JGL}. This feature is still in development, it may not work as intended, especially if using parallel computing.

Value

jgl	The output of JGL
lambda1	the value of lambda 1 that minimizes the output of aicfun
l1theormax	the minimal value of lambda 1 that would result in at least one completely disconnected network (all missing edges). Values of lambda 1 > l1theormax are not considered
l2theormax	for each candidate value of lambda 1, the minimal value of lambda 2 that would make the networks in the different classes all equal to each other. For each lambda 1, values of lambda 2 > l2theormax are not considered
aic	The Akaike Information Criterion (or the output of another function passed to aicfun) corresponding to the solution in jgl

Author(s)

Giulio Costantini

References

Danaher, P., Wang, P., & Witten, D. M. (2014). The joint graphical lasso for inverse covariance estimation across multiple classes. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76(2), 373-397. http://doi.org/10.1111/rssb.12033 Guo, J., Levina, E., Michailidis, G., & Zhu, J. (2011). Joint estimation of multiple graphical models. Biometrika, 98(1), 1-15. http://doi.org/10.1093/biomet/asq060

See Also

JGL, JGL_AIC_sequentialsearch, JGL_AIC_widesearch, JGL_AIC_surfaceplot

Examples

## Not run: 
N <- 1000 # sample size
sigma1 <- matrix(c(1, .5, 0, 0,
                  .5, 1, .2, 0,
                  0, .2, 1, 0,
                  0, 0, 0, 1), ncol = 4)

sigma2 <- matrix(c(1, .5, .4, .4,
                   .5, 1, .2, 0,
                   .4, .2, 1, 0,
                   .4, 0, 0, 1), ncol = 4)


dat <- list()
dat[[1]] <- MASS::mvrnorm(n = N, mu = rep(0, ncol(sigma1)), Sigma = sigma1)
dat[[2]] <- MASS::mvrnorm(n = N, mu = rep(0, ncol(sigma2)), Sigma = sigma2)
lapply(dat, function(x) corpcor::cor2pcor(cor(x)))
dat <- data.frame(rbind(dat[[1]], dat[[2]]))
dat$splt <- c(rep(1, N), rep(2, N))
splt <- "splt"

x <- JGL_cv(dat = dat, splt = splt, ncand = 20, l2max = 1, seed = 1, k = 10, ncores = 7, aicfun = AIC)
x

## End(Not run)

GiulioCostantini/JGL2 documentation built on May 6, 2019, 6:29 p.m.