dpcid (version 1.0)

dpcid_core: Identification of two partial correlation matrices having sparse differences

Description

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

Usage

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

Arguments

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.

Value

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.

Details

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.

References

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.

Examples

# NOT RUN {
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)
    
# }