ECV.block: selecting block models by ECV

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

selecting block models by ECV

Description

Model selection by ECV for SBM and DCSBM. It can be used to select between the two models or given on model (either SBM or DCSBM) and select K.

Usage

ECV.block(A, max.K, cv = NULL, B = 3, holdout.p = 0.1, tau = 0, dc.est = 2, kappa = NULL)

Arguments

A	adjacency matrix
max.K	largest possible K for number of communities
cv	cross validation fold. The default value is NULL. We recommend to use the argument B instead, doing indpendent sampling.
B	number of replications
holdout.p	testing set proportion
tau	constant for numerical stability only. Not useful for current version.
dc.est	estimation method for DCSBM. By defaulty (dc.est=2), the maximum likelihood is used. If dc.est=1, the method used by Chen and Lei (2016) is used, which is less stable according to our observation.
kappa	constant for numerical stability only. Not useful for current version.

Details

The current version is based on a simple matrix completion procedure, as described in the paper. The performance can be improved by better matrix completion method that will be implemented in next version. Moreover, the current implementation is better in computational time but less efficient in memory. Another memory efficient implementation will be added in next version.

Value

impute.err	average validaiton imputation error
l2	average validation L_2 loss under SBM
dev	average validation binomial deviance loss under SBM
auc	average validation AUC
dc.l2	average validation L_2 loss under DCSBM
dc.dev	average validation binomial deviance loss under DCSBM
sse	average validation SSE
l2.model	selected model by L_2 loss
dev.model	selected model by binomial deviance loss
l2.mat, dc.l2.mat,...	cross-validation loss matrix for B replications

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.

See Also

NCV.select

Examples

dt <- BlockModel.Gen(30,300,K=3,beta=0.2,rho=0.9,simple=FALSE,power=TRUE)


A <- dt$A

ecv <- ECV.block(A,6,B=3)

ecv$l2.model
ecv$dev.model


which.min(ecv$l2)
which.min(ecv$dev)

which.min(ecv$dc.l2)
which.min(ecv$dc.dev)

which.max(ecv$auc)
which.min(ecv$sse)

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