Stability Selection

Here, we demonstrate the stability selection technique to learn the network sparsity for networks estimated via the LPGM method.

We simulate a scale-free network with 30 variables and 200 observations. We determine the network sparsity based on the stability score, which retains network edges that are estimated in more than 95% (sth=0.95) of the 50 bootstrap repetitions (N=50). The code is given below:

> library(XMRF)
> n = 200
> p = 30
  
# Simulate a scale-free network of 30 notes and 200 samples
> sim <- XMRF.Sim(n=n, p=p, model="LPGM", graph.type="scale-free")
> simDat <- sim$X
   
# Compute the optimal lambda
> lmax = lambdaMax(t(simDat))
> lambda = 0.01* sqrt(log(p)/n) * lmax
   
# Run Local Poisson Graphical Model (LPGM)
> lpgm.fit <- XMRF(simDat, method="LPGM", lambda.path=lambda, sth=0.95, N=50)

Results for the code above are shown in Figure S5. It shows that the estimated network structure (Figure S5(B)) is equivalent to the true network structure (Figure S5(A)). Note that stability selection is the default way to determine network sparsity in XMRF.

Figure S5: Simulated network from XMRF.Sim(...,model="LPGM") (A) and inferred network estimated via XMRF(...,method="LPGM") with network sparsity determined via stability selection (B).