estimateScoreSBM: Inference of the Score SBM Model

In Sophiedonnet/NoisySBM: Inference of a network topology from a one or several noisy version(s) of the network

Description

estimateScoreSBM performs the estimation and model selection for the ScoreSBM model.

Usage

estimateScoreSBM(
  scoreList,
  directed = FALSE,
  nparm = FALSE,
  kerSigma = NULL,
  estimOptions = list(),
  monitoring = list()
)

Arguments

scoreList	: list of Scores for each dyad of an underlying network
directed	: Boolean. If true the inference network is directed. Default value = FALSE.
nparm	: Boolean. If true then the emission distribution is Non Parametric (Default value FALSE)
kerSigma	: Plug-in bandwidth for non-parametric estimation. If not provided, will be estimated with Hpi (up to six scores). Default value is null
estimOptions	: tunes the optimization process (see details below)
monitoring	: specifies if the lowerBound along the VEM iterations is saved (monitoring = list(lowerBound = TRUE))

Details

The list of parameters estimOptions essentially tunes the optimization process and the variational EM algorithm, with the following parameters

• "verbosity" controls the verbosity of the procedure (0, 1 or 2). Default is 1.

• "exploreFactor" controls the exploration of the number of groups in the initialization step, Default is 1.5

• "nbBlocksRange" minimal and maximal number or blocks explored. Default is c(1,Inf)

• "nbCores" integer for number of cores used. Default is 1.

• "maxIterVE" Maximum number of iterations in the VE step. Default is 100.

• "maxIterVE" Maximum number of iterations in the VEM algorithm. Default is 1000.

• "tauTol" Tolerance in the VEM algorithm. Default value tauTol = 2 * .Machine$double.eps

• "etaTol" Tolerance in the VEM algorithm. Default value etaTol = 2 * .Machine$double.eps

• "valCritStop" Algorithm stops when the difference on successive tau is below valCritStop. Default value is 1e-6

Each element of the output list contains the following quantites:

• "theta"estimated parameters

• "nbBlocks" number of blocks in the underlying network

• "qDist" variational approximation of the the conditional distribution q(G,Z | data)

• "ICL": Integrated Likelihood Criterion

• "pen": Penalty term for model selection (included in the ICL)

• "lowerBound": Lowerbound along the VEM iterations (provided if monitoring$lowerBound = TRUE)

Value

The output is a list of estimated models, each one corresponding to a number of blocks.

Examples

nbNodes  <- 60
directed <- FALSE
blockProp <- c(1/3,1/2,1/6)
nbBlocks   <- length(blockProp)
connectParam <- matrix(rbeta(nbBlocks^2,1.5,1.5 ),nbBlocks,nbBlocks)
connectParam <- 0.5*(connectParam + t(connectParam))
emissionParam <- list()
nbScores <- 4
emissionParam$noEdgeParam <- list(mean=rep(0,nbScores));
emissionParam$noEdgeParam$var <- diag(0.1,nrow = nbScores,ncol = nbScores)
emissionParam$edgeParam <- list( mean= 1:nbScores)
emissionParam$edgeParam$var <-  diag(0.1,nrow = nbScores,ncol = nbScores)
dataSim <- rScoreSBM(nbNodes,directed = TRUE, blockProp,connectParam,emissionParam,seed = NULL)
scoreList <- dataSim$scoreNetworks
resEstim <- estimateScoreSBM(scoreList,directed)

Sophiedonnet/NoisySBM documentation built on Oct. 20, 2020, 12:04 p.m.