crit.dpcid: Akaike information criterion (AIC) and Bayesian information...
In dpcid: Differential Partial Correlation IDentification

Description Usage Arguments Details Value References Examples

aic.dpcid returns the AIC values corresponding to the given lambda1 and lambda2 values for the DPCID.

1	crit.dpcid(A,B,l1,seq_l2,wd1,wd2,rho1_init,rho2_init,niter=1000,tol=1e-6,scaling=FALSE)

`A`	An observed dataset from the first condition.
`B`	An observed dataset from the second condition.
`l1`	The selected lambda1 in cv.lambda1.
`seq_l2`	A sequence of tuning parameter lambda2 for the fusion penalty
`wd1`	The estimate of diagonal elements of the precision matrix of the first condition.
`wd2`	The estimate of diagonal elements of the precision matrix of the second condition.
`rho1_init`	An initial value for the partial correlation matrix of the first condition.
`rho2_init`	An initial value for the partial correlation matrix of the second condition.
`niter`	A total number of iterations in the block-wise coordinate descent.
`tol`	A tolerance for the convergence.
`scaling`	a logical flag for scaling variable to have unit variance. Default is FALSE.

crit.dpcid needs the estimates of the diagonal elements of two precision matrices.

`aic`	A vector of aic values corresponding to a given sequence of tuning paramters.
`bic`	A vector of bic values corresponding to a given sequence of tuning paramters.

Yu, D., Lee, S. H., Lim, J., Xiao, G., Craddock, R. C., and Biswal, B. B. (2018). Fused Lasso Regression for Identifying Differential Correlations in Brain Connectome Graphs. Statistical Analysis and Data Mining, 11, 203–226.

library(MASS)

## True precision matrix
omega1 <- matrix(0,5,5)
omega1[1,2] <- omega1[1,3] <- omega1[1,4] <- 1
omega1[2,3] <- omega1[3,4] <- 1.5
omega1 <- t(omega1) + omega1
diag(omega1) <- 3

omega2 <- matrix(0,5,5)
omega2[1,3] <- omega2[1,5] <- 1.5
omega2[2,3] <- omega2[2,4] <- 1.5
omega2 <- t(omega2) + omega2
diag(omega2) <- 3

Sig1 = solve(omega1)
Sig2 = solve(omega2)
X1 = mvrnorm(50,rep(0,5),Sig1)
X2 = mvrnorm(50,rep(0,5),Sig2)

A = scale(X1,center=TRUE,scale=FALSE)
B = scale(X2,center=TRUE,scale=FALSE)

shr_res = lshr.cov(A)
PM1 = shr_res$shr_inv

shr_res = lshr.cov(B)
PM2 = shr_res$shr_inv

wd1 = diag(PM1)
wd2 = diag(PM2)

rho1_init = -(1/sqrt(wd1))*PM1
rho1_init = t( 1/sqrt(wd1)*t(rho1_init))
diag(rho1_init) = 1

rho2_init = -(1/sqrt(wd2))*PM2
rho2_init = t( 1/sqrt(wd2)*t(rho2_init))
diag(rho2_init) = 1

l1 = 0.3
seq_l2 = seq(0.1,1,by=0.2)

crit =crit.dpcid(A,B,l1,seq_l2,wd1,wd2,rho1_init,rho2_init)
crit$aic
crit$bic