Description Usage Arguments Details Value Author(s) See Also Examples
Implements the data generation from multivariate normal distributions with different graph structures, including "random"
, "hub"
, "cluster"
and "band"
.
1 2 |
n |
The number of observations (sample size). The default value is |
d |
The number of variables (dimension). The default value is |
graph |
The graph structure with 4 options: |
v |
The off-diagonal elements of the precision matrix, controlling the magnitude of partial correlations with |
u |
A positive number being added to the diagonal elements of the precision matrix, to control the magnitude of partial correlations. The default value is |
g |
For |
prob |
For |
vis |
Visualize the adjacency matrix of the true graph structure, the graph pattern, the covariance matrix and the empirical covariance matrix. The default value is |
verbose |
If |
Given the adjacency matrix theta
, the graph patterns are generated as below:
(I) "random"
: Each pair of off-diagonal elements are randomly set theta[i,j]=theta[j,i]=1
for i!=j
with probability prob
, and 0
other wise. It results in about d*(d-1)*prob/2
edges in the graph.
(II)"hub"
:The row/columns are evenly partitioned into g
disjoint groups. Each group is associated with a "center" row i
in that group. Each pair of off-diagonal elements are set theta[i,j]=theta[j,i]=1
for i!=j
if j
also belongs to the same group as i
and 0
otherwise. It results in d - g
edges in the graph.
(III)"cluster"
:The row/columns are evenly partitioned into g
disjoint groups. Each pair of off-diagonal elements are set theta[i,j]=theta[j,i]=1
for i!=j
with the probability prob
if both i
and j
belong to the same group, and 0
other wise. It results in about g*(d/g)*(d/g-1)*prob/2
edges in the graph.
(IV)"band"
: The off-diagonal elements are set to be theta[i,j]=1
if 1<=|i-j|<=g
and 0
other wise. It results in (2d-1-g)*g/2
edges in the graph.
The adjacency matrix theta
has all diagonal elements equal to 0
. To obtain a positive definite precision matrix, the smallest eigenvalue of theta*v
(denoted by e
) is computed. Then we set the precision matrix equal to theta*v+(|e|+0.1+u)I
. The covariance matrix is then computed to generate multivariate normal data.
An object with S3 class "sim" is returned:
data |
The |
sigma |
The covariance matrix for the generated data |
omega |
The precision matrix for the generated data |
sigmahat |
The empirical covariance matrix for the generated data |
theta |
The adjacency matrix of true graph structure (in sparse matrix representation) for the generated data |
Haotian Pang, Han Liu and Robert Vanderbei
Maintainer: Haotan Pang<hpang@princeton.edu>
fastclime
and fastclime-package
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ## band graph with bandwidth 3
L = fastclime.generator(graph = "band", g = 3)
plot(L)
## random sparse graph
L = fastclime.generator(vis = TRUE)
## random dense graph
L = fastclime.generator(prob = 0.5, vis = TRUE)
## hub graph with 6 hubs
L = fastclime.generator(graph = "hub", g = 6, vis = TRUE)
## hub graph with 8 clusters
L = fastclime.generator(graph = "cluster", g = 8, vis = TRUE)
|
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