ECV.nSmooth.lowrank: selecting tuning parameter for neighborhood smoothing...

In randnet: Random Network Model Estimation, Selection and Parameter Tuning

selecting tuning parameter for neighborhood smoothing estimation of graphon model

Description

selecting tuning parameter for neighborhood smoothing estimation of graphon model where the tuning parameter is to control estimation smoothness.

Usage

ECV.nSmooth.lowrank(A, h.seq, K, cv = NULL, B = 3, holdout.p = 0.1)

Arguments

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

Details

The neighborhood smoothing estimation can be slow, so the ECV may take long even for moderately large networks.

Value

a list object with

err	average validation error for h.seq
min.index	index of the minimum error

Author(s)

Tianxi Li, Elizaveta Levina, Ji Zhu
Maintainer: Tianxi Li [e-mail]

References

T. Li, E. Levina, and J. Zhu. Network cross-validation by edge sampling. Biometrika, 107(2), pp.257-276, 2020.

Examples

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


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) 

h <- h.seq[ecv.nsmooth$min.index]

randnet documentation built on May 31, 2023, 6:44 p.m.