space.neighbor: A function to estimate partial correlations using the...
In space: Sparse PArtial Correlation Estimation

Description Usage Arguments Details Value Author(s) References Examples

View source: R/space.R

A function to estimate partial correlations using the neighborhood selection approach

1	space.neighbor(Y.m, lam1, lam2=0)

`Y.m`	numeric matrix. Each column is for one variable and each row is for one sample. Missing values are not allowed. It's recommended to first standardize each column to have mean 0 and norm 1.
`lam1`	numeric value. This is the l_1 norm penalty parameeter. If the columns of Y.m have norm one, then the suggested range of lam1 is: O(n^{1/2}Φ^{-1}(1-α/(2p^2))) for small α such as 0.1.
`lam2`	numeric value. If not specified, lasso regression is used in the neighborhood selection. Otherwise, elastic net regression is used and `lam2` serves as the l_2 norm penalty parameter.

space.neighbor estimate partial correlations using the neighborhood selection approach (Meinshausen and Buhlmann, 2006).

A list with two components

`ParCor`	the estimated partial correlation matrix.
`sig.fit`	numeric vector of the estimated σ^{ii}

J. Peng, P. Wang, N. Zhou, J. Zhu

J. Peng, P. Wang, N. Zhou, J. Zhu (2007). Partial Correlation Estimation by Joint Sparse Regression Model.

Meinshausen, N., and Buhlmann, P. (2006), High Dimensional Graphs and Variable Selection with the Lasso, Annals of Statistics, 34, 1436-1462.

#############################################################################################
############################ (A) The simulated Hub.net example in Peng et. al. (2007).
#############################################################################################
data(spaceSimu)

n=nrow(spaceSimu$Y.data)
p=ncol(spaceSimu$Y.data)
true.adj=abs(spaceSimu$ParCor.true)>1e-6

#################### view the network corresponding to the parcial correlation matrix in the simulation example
#################### view the network corresponding to the parcial correlation matrix in the simulation example
########### the following code can run only if the "igraph" is installed in the system.
#library(igraph)
#plot.adj=true.adj
#diag(plot.adj)=0
#temp=graph.adjacency(adjmatrix=plot.adj, mode="undirected")
#temp.degree=apply(plot.adj, 2, sum)
#V(temp)$color=(temp.degree>9)+3
#plot(temp, vertex.size=3, vertex.frame.color="white",layout=layout.fruchterman.reingold, vertex.label=NA, edge.color=grey(0.5))


#################### estimate the parcial correlation matrix with various methods
alpha=1
l1=1/sqrt(n)*qnorm(1-alpha/(2*p^2))
iter=3


########### the values of lam1 were selected to make the results of different methods comparable. 
#### 1. MB method
result1=space.neighbor(spaceSimu$Y.data, lam1=l1*0.7, lam2=0)
fit.adj=abs(result1$ParCor)>1e-6
sum(fit.adj==1)/2                  ##total number of edges detected      
sum(fit.adj[true.adj==1]==1)/2  ##total number of true edges detected        
 
#### 2. Joint method with no weight
result2=space.joint(spaceSimu$Y.data, lam1=l1*n*1.56, lam2=0, iter=iter)
fit.adj=abs(result2$ParCor)>1e-6
sum(fit.adj==1)/2                  ##total number of edges detected      
sum(fit.adj[true.adj==1]==1)/2  ##total number of true edges detected        

#### 3. Joint method with residue variance based weights
result3=space.joint(spaceSimu$Y.data, lam1=l1*n*1.86, lam2=0, weight=1, iter=iter)
fit.adj=abs(result3$ParCor)>1e-6
sum(fit.adj==1)/2                  ##total number of edges detected      
sum(fit.adj[true.adj==1]==1)/2  ##total number of true edges detected        

#### 4. Joint method with degree based weights
result4=space.joint(spaceSimu$Y.data, lam1=l1*n*1.61, lam2=0, weight=2, iter=iter)
fit.adj=abs(result4$ParCor)>1e-6
sum(fit.adj==1)/2                  ##total number of edges detected      
sum(fit.adj[true.adj==1]==1)/2  ##total number of true edges detected