selecting tuning parameter for neighborhood smoothing estimation of graphon model
selecting tuning parameter for neighborhood smoothing estimation of graphon model where the tuning parameter is to control estimation smoothness.
ECV.nSmooth.lowrank(A, h.seq, K, cv = NULL, B = 3, holdout.p = 0.1)
A |
adjacency matrix |
h.seq |
a sequence of h values to tune. It is suggested h should be in the order of sqrt(log(n)/n). |
K |
the optimal rank for approximation. Can be obtained by rank selection of ECV. |
cv |
cross-validation fold. Recomend to use replication number B instead. |
B |
independent replication number of random splitting |
holdout.p |
proportion of test sample |
The neighborhood smoothing estimation can be slow, so the ECV may take long even for moderately large networks.
a list object with
err |
average validation error for h.seq |
min.index |
index of the minimum error |
Tianxi Li, Elizaveta Levina, Ji Zhu
Maintainer: Tianxi Li tianxili@umich.edu
T. Li, E. Levina, and J. Zhu. Network cross-validation by edge sampling. arXiv preprint arXiv:1612.04717, 2016.
set.seed(500) N <- 300 U = matrix(1:N,nrow=1) / (N+1) V = matrix(1:N,nrow=1) / (N+1) W = (t(U))^2 W = W/3*cos(1/(W + 1e-7)) + 0.15 upper.index <- which(upper.tri(W)) A <- matrix(0,N,N) rand.ind <- runif(length(upper.index)) edge.index <- upper.index[rand.ind < W[upper.index]] A[edge.index] <- 1 A <- A + t(A) diag(A) <- 0 #ecv.rank <- ECV.Rank(A,10,B=3,weighted=FALSE,mode="undirected") #K.hat <- ecv.rank$auc.rank ## first estimate a good rank #h.seq <- sqrt(log(N)/N)*seq(0.5,5,by=0.5) #ecv.nsmooth <- ECV.nSmooth.lowrank(A,h.seq,K=2,B=3) ## nSmooth can be slow #h <- h.seq[ecv.nsmooth$min.index] #What <- nSmooth(A,h=h) #par(mfrow=c(1,2)) #image(t(W[N:1,])) #image(t(What[N:1,]))
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