ECV.block: 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)

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

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.

Author

Tianxi Li, Elizaveta Levina, Ji Zhu
Maintainer: Tianxi Li tianxili@virginia.edu

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.

References

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

Examples

Run this code


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)

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