dpcid_core: Identification of two partial correlation matrices having...
In dpcid: Differential Partial Correlation IDentification

Description Usage Arguments Details Value References Examples

dpcid_core estimates two partial correlation matrices by applying the regression approach with the ridge penalty and the fusion penalty.

1	dpcid_core(A,B,lambda1,lambda2,wd1,wd2,rho1_init,rho2_init,niter=1000,tol=1e-6)

`A`	An observed dataset from the first condition.
`B`	An observed dataset from the second condition.
`lambda1`	A tuning parameter for the ridge penalty.
`lambda2`	A a tuning parameter for the fusion penalty between two precision matrices.
`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.

Dpcid_core is the partial correaltion step of the differential partial correlation identification method by Yu et al.(2018). The dpcid_core estimates two partial correlation matrices with the estimated diagonal elements of two precision matrices from the optimal linear shrinkage estimates. The estimated precision matrices by the optimal linear shrinkage estimates can simply be used as the initial values of PM1 and PM2 in the dpcid_core.

`rho1`	An estimated partial correlatioin matrix of the first condition.
`rho2`	An estimated partial correlatioin matrix of the second condition.
`resid1`	Residuals of the first condtion.
`resid2`	Residuals of the second condtion.

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)

lambda1 = 1
lambda2 = 1

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

res = dpcid_core(A, B, lambda1, lambda2, wd1,wd2, rho1_init, rho2_init)