fitNSBM: VEM algorithm to adjust the noisy stochastic block model to...
In noisySBM: Noisy Stochastic Block Mode: Graph Inference by Multiple Testing

Description Usage Arguments Details Value Examples

fitNSBM() estimates model parameters of the noisy stochastic block model and provides a clustering of the nodes

fitNSBM(
  dataMatrix,
  model = "Gauss0",
  sbmSize = list(Qmin = 1, Qmax = NULL, explor = 1.5),
  filename = NULL,
  initParam = list(nbOfTau = NULL, nbOfPointsPerTau = NULL, maxNbOfPasses = NULL,
    minNbOfPasses = 1),
  nbCores = parallel::detectCores()
)

`dataMatrix`	observed dense adjacency matrix
`model`	Implemented models: `Gauss` all Gaussian parameters of the null and the alternative distributions are unknown ; this is the Gaussian model with maximum number of unknown parameters `Gauss0` compared to `Gauss`, the mean of the null distribution is set to 0 `Gauss01` compared to `Gauss`, the null distribution is set to N(0,1) `GaussEqVar` compared to `Gauss`, all Gaussian variances (of both the null and the alternative) are supposed to be equal, but unknown `Gauss0EqVar` compared to `GaussEqVar`, the mean of the null distribution is set to 0 `Gauss0Var1` compared to `Gauss`, all Gaussian variances are set to 1 and the null distribution is set to N(0,1) `Gauss2distr` the alternative distribution is a single Gaussian distribution, i.e. the block memberships of the nodes do not influence on the alternative distribution `GaussAffil` compared to `Gauss`, for the alternative distribution, there's a distribution for inter-group and another for intra-group interactions `Exp` the null and the alternatives are all exponential distributions (i.e. Gamma distributions with shape parameter equal to one) with unknown scale parameters `ExpGamma` the null distribution is an unknown exponential, the alterantive distribution are Gamma distributions with unknown parameters
`sbmSize`	list of parameters determining the size of SBM (the number of latent blocks) to be expored `Qmin` minimum number of latent blocks `Qmax` maximum number of latent blocks `explor` if `Qmax` is not provided, then `Qmax` is automatically determined as `explor` times the number of blocks where the ICL is maximal
`filename`	results are saved in a file with this name (if provided)
`initParam`	list of parameters that fix the number of initializations `nbOfTau` number of initial points for the node clustering (i. e. for the variational parameters `tau`) `nbOfPointsPerTau` number of initial points of the latent binary graph `maxNbOfPasses` maximum number of passes through the SBM models, that is, passes from `Qmin` to `Qmax` or inversely `minNbOfPasses` minimum number of passes through the SBM models
`nbCores`	number of cores used for parallelization

fitNSBM() supports different probability distributions for the edges and can estimate the number of node blocks

Returns a list of estimation results for all numbers of latent blocks considered by the algorithm. Every element is a list composed of:

theta

estimated parameters of the noisy stochastic block model; a list with the following elements:

pi: parameter estimate of pi
w: parameter estimate of w
nu0: parameter estimate of nu0
nu: parameter estimate of nu

clustering

node clustering obtained by the noisy stochastic block model, more precisely, a hard clustering given by the maximum aposterior estimate of the variational parameters sbmParam$edgeProba

sbmParam

further results concerning the latent binary stochastic block model. A list with the following elements:

Q: number of latent blocks in the noisy stochastic block model
clusterProba: soft clustering given by the conditional probabilities of a node to belong to a given latent block. In other words, these are the variational parameters tau; (Q x n)-matrix
edgeProba: conditional probabilities rho of an edges given the node memberships of the interacting nodes; (N_Q x N)-matrix
ICL: value of the ICL criterion at the end of the algorithm

convergence

a list of convergence indicators:

J: value of the lower bound of the log-likelihood function at the end of the algorithm
complLogLik: value of the complete log-likelihood function at the end of the algorithm
converged: indicates if algorithm has converged
nbIter: number of iterations performed

n <- 10
theta <- list(pi= c(0.5,0.5), nu0=c(0,.1),
       nu=matrix(c(-2,10,-2, 1,1,1),3,2),  w=c(.5, .9, .3))
obs <- rnsbm(n, theta, modelFamily='Gauss')
res <- fitNSBM(obs$dataMatrix, sbmSize = list(Qmax=3),
       initParam=list(nbOfTau=1, nbOfPointsPerTau=1), nbCores=1)