A simulation of a hub network in the high-dimension and low sample size regime. @details The variables are as follows:
data(sim1)
A list of data elements Y,X,truth.
Y Numeric matrix of 150 iid samples of 171 of response variables.
X Numeric matrix of 150 iid samples of 14 predictor variables.
truth List containing
xy Adjacency matrix encoding \(x-y\) edges.
yy Adjacency matrix encoding \(y-y\) edges.
The simulation contains response variables \(Y = (y_1, \dots, y_Q)\) and predictor variables \(X = (x_1, \dots, x_P)\), where \(P=14,Q=171\). \(N=150\) iid samples were drawn from \((X,Y) ~ N(0, \Theta^{-1})\) where non-zero off-diagonal elements of \(\Theta\) encode the edges of the hub network. The network contains 10 predictors that have no edges at all, while 2 hub predictors have 13 \(x-y\) edges and 2 other hub predictors have 14 \(x-y\) edges. Among the response edges \(y-y\), there are 2 hub variables with degree 12 and 13, but the degree of the other response variables does not exceed 4. There are two disconnected components in the graph of size 94 and 81. The data has been standardized (mean-centered with unit variance) for all variables.