equSA (version 1.2.1)

GraphIRO: Learning high-dimensional Gaussian Graphical Models with Missing Observations.

Description

The imputation regularized optimization (IRO) algorithm for learning high-dimensional Gaussian Graphical Models from incomplete dataset.

Usage

GraphIRO(data, A, alpha1 = 0.05, alpha2 = 0.05, alpha3 = 0.05, iteration = 30, warm = 10)

Arguments

data

\(n\)x\(p\) Dataset with missing values.

A

True adjacency matrix for evaluating the performance of the IRO algorithm.

alpha1

The significance level of correlation screening in the \(\psi\)-learning algorithm, see R package equSA for detail. In general, a high significance level of correlation screening will lead to a slightly large separator set, which reduces the risk of missing important variables in the conditioning set. In general, including a few false variables in the conditioning set will not hurt much the accuracy of the \(\psi\)-partial correlation coefficient, the default value is 0.05.

alpha2

The significance level of \(\psi\)-partial correlation coefficient screening for estimating the adjacency matrix, see equSA, the default value is 0.05.

alpha3

The significance level of integrative \(\psi\)-partial correlation coefficient screening for estimating the adjacency matrix of IRO_Ave method, the default value is 0.05.

iteration

The number of total iterations, the default value is 30.

warm

The number of burn-in iterations, the default value is 10.

Value

RecPre

The output of Recall and Precision values for the IRO algorithm.

Adj

\(p\)x\(p\) Estimated adjacency matrix by our IRO algorithm.

%% ...

References

Liang, F., Song, Q. and Qiu, P. (2015). An Equivalent Measure of Partial Correlation Coefficients for High Dimensional Gaussian Graphical Models. J. Amer. Statist. Assoc., 110, 1248-1265.

Liang, F. and Zhang, J. (2008) Estimating FDR under general dependence using stochastic approximation. Biometrika, 95(4), 961-977.

Liang, F., Jia, B., Xue, J., Li, Q., and Luo, Y. (2018). An Imputation Regularized Optimization Algorithm for High-Dimensional Missing Data Problems and Beyond. Submitted to Journal of the Royal Statistical Society Series B.

Examples

# NOT RUN {
 
# }
# NOT RUN {
library(equSA)
result <- SimGraDat(n = 200, p = 100, type = "band", rate = 0.1)
Est <- GraphIRO(result$data, result$A, iteration = 20, warm = 10)
## plot network by our estimated adjacency matrix.
plotGraph(Est$Adj)  
## plot the Recall-Precision curve.
plot(Est$RecPre[,1], Est$RecPre[,2], type="l", xlab="Recall", ylab="Precision")  

# }
# NOT RUN {
# }