huge (version 0.7)

huge.generator: Data generating function

Description

Implements the data generator from multivariate normal distributions with different graph structures, including "random", "hub", "clique" or "band".

Usage

huge.generator(n = 200, d = 50, graph = "random", v = NULL, u = NULL, 
g = NULL, prob = 0.03, vis = FALSE, verbose = TRUE)

Arguments

n

The number of observations (sample size). The default value is 200.

d

The number of variables (dimension). The default value is 50.

graph

The graph structure with 4 options: "random", "hub", "clique" and "band".

v

The off-diagonal elements of the precision matrix, controlling the magnitude of partial correlations with u. The default value is 0.1 for "band" and 0.3 for "random", "hub",

u

A positive number (with a default value 0.5) being added to the diagonal elements of the precision matrix, to control the magnitude of partial correlations. The default value is 0 for "clique" and 1 for "rando

g

For "clique" or "hub" graph, g is the number of hubs or cliques in the graph: when "graph = hub" default value is about d/8 if d >= 16 and 2 if d<16< code="">; w

prob

The probability that a pair of nodes has an edge. The default value is 0.03. Only applicable when the graph pattern is "random".

vis

Visualize the adjacency matrix of the true graph structure, the graph pattern, the covariance matrix and the precision matrix. The default value is FALSE

verbose

If verbose = FALSE, tracing information printing is disabled. The default value is TRUE.

Value

• An object with S3 class "sim" is returned:
• data
  The n by d matrix for the generated data
• sigma
  The covariance matrix for the generated data
• omega
  The precision matrix for the generated data
• theta
  The adjacency matrix of true graph structure (in sparse matrix representation) for the generated data

Details

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)"clique":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 if both i and j belong to the same group, and 0 other wise. It results in about g(d/g)(d/g-1)/2 edges in the graph. (IV)"band": The off-diagonal elements are set to be theta[i,j]=1 if 1<=|i-j|<=g< code=""> 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 is computed. Suppose e be the smallest eigenvalue and we let the precision matrix equals theta*v+(|e|+0.01+t)I. The covariance matrix is then computed to generate multivariate normal data.

References

Tuo Zhao and Han Liu. HUGE: A Package for High-dimensional Undirected Graph Estimation. Technical Report, Carnegie Mellon University, 2010 Jerome Friedman, Trevor Hastie and Rob Tibshiran. Applications of the lasso and grouped lasso to the estimation of sparse graphical models, Technical Report, Stanford University, 2010

See Also

huge and huge-package

Examples

# band graph with bandwidth 3
L = huge.generator(n = 500, graph = "band", g = 3)
summary(L)
plot(L)

# random sparse graph
L = huge.generator(prob = 0.05, vis = TRUE)

# random dense graph
L = huge.generator(prob = 0.3, vis = TRUE)

# hub graph with 4 hubs
L = huge.generator(graph = "hub", g = 4, vis = TRUE)