Estimation of Simple SBMs — estimateSimpleSBM • sbm

This function performs variational inference of simple Stochastic Block Models, with various model for the distribution of the edges: Bernoulli, Poisson, or Gaussian models.

Usage

estimateSimpleSBM(
  netMat,
  model = "bernoulli",
  directed = !isSymmetric(netMat),
  dimLabels = c("node"),
  covariates = list(),
  nodesCovariates = matrix(0, 0, 0),
  estimOptions = list()
)

Arguments

netMat: a matrix describing the network: either an adjacency (square) or incidence matrix with possibly weighted entries.
model: character describing the model for the relation between nodes ('bernoulli', 'poisson', 'gaussian', ...). Default is 'bernoulli'.
directed: logical: is the network directed or not? Only relevant when type is 'Simple'. Default is TRUE if netMat is symmetric, FALSE otherwise
dimLabels: an optional label for referring to the nodes
covariates: a list of matrices with same dimension as mat describing covariates at the edge level. No covariate per Default.
nodesCovariates: a matrix with the same number of rows as the number of nodes in the network, describing the nodes covariates. No nodes covariates per default.
estimOptions: a list of parameters controlling the inference algorithm and model selection. See details.

Value

a list with the estimated parameters. See details...

Details

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

"nbCores integer for number of cores used. Default is 2 (1 under Positron, which does not allow forking)
"verbosity" integer for verbosity (0, 1). Default is 1
"plot" boolean, should the ICL be dynamically plotted or not. Default is TRUE, FALSE when "verbosity" is 0
"exploreFactor" control the exploration of the number of groups
"exploreMin" explore at least until exploreMin even if the exploration factor rule is achieved. Default 4. See the package blockmodels for details.
"exploreMax" Stop exploration at exploreMax even if the exploration factor rule is not achieved. Default Inf. See the package blockmodels for details.
"nbBlocksRange" minimal and maximal number or blocks explored
"fast" logical: should approximation be used for Bernoulli model with covariates. Default to TRUE
"explorationDirection" (only used for BipartiteSBM) a vector of two integers which controls the exploration direction for groups number. When provided, the exploring strategy is made to explore the provided group number. The two integer value representing the row group number and the column group number.

Missing values

The network netMat may contain missing values (NA): the corresponding dyads are considered as not observed. They are ignored in the likelihood, in the estimation of the parameters and in the ICL, whose penalty only counts the observed dyads. This assumes that the dyads are missing at random; for other sampling designs, see the package missSBM. The diagonal of the adjacency matrix of a simple network is ignored.

Examples

### =======================================
### SIMPLE BINARY SBM (Bernoulli model)

## Graph parameters & Sampling
nbNodes  <- 60
blockProp <- c(.5, .25, .25) # group proportions
means <- diag(.4, 3) + 0.05  # connectivity matrix: affiliation network
connectParam <- list(mean = means)
mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam)
adjacencyMatrix <- mySampler$networkData

## Estimation
mySimpleSBM <-
  estimateSimpleSBM(adjacencyMatrix, 'bernoulli', estimOptions = list(plot = FALSE, nbCores = 1))
#> -> Estimation for 1 groups
#> 
-> Computation of eigen decomposition used for initalizations
#> -> Pass 1
#>     -> With ascending number of groups
#>         -> For 2 groups
#> 
        -> For 3 groups
#> 
        -> For 4 groups
#> 
        -> For 5 groups
#> 
    -> With descending number of groups
#>         -> For 4 groups
#> 

        -> For 3 groups
#> 
        -> For 2 groups
#> 
-> Pass 2
#>     -> With ascending number of groups
#>         -> For 2 groups
#>         -> For 3 groups
#>         -> For 4 groups
#>         -> For 5 groups
#> 
    -> With descending number of groups
#>         -> For 4 groups
#>         -> For 3 groups
#>         -> For 2 groups
#> -> Pass 3
#>     -> With ascending number of groups
#>         -> For 2 groups
#>         -> For 3 groups
#>         -> For 4 groups
#>         -> For 5 groups
#>     -> With descending number of groups
#>         -> For 4 groups
#>         -> For 3 groups
#>         -> For 2 groups
plot(mySimpleSBM, 'data', ordered = FALSE)

plot(mySimpleSBM, 'data')

plot(mySimpleSBM, 'expected', ordered = FALSE)

plot(mySimpleSBM, 'expected')

plot(mySimpleSBM, 'meso')


### =======================================
### SIMPLE POISSON SBM

## Graph parameters & Sampling
nbNodes  <- 60
blockProp <- c(.5, .25, .25) # group proportions
means <- diag(15., 3) + 5    # connectivity matrix: affiliation network
connectParam <- list(mean = means)
mySampler <- sampleSimpleSBM(nbNodes, blockProp, list(mean = means), model = "poisson")
adjacencyMatrix <- mySampler$networkData

## Estimation
mySimpleSBM <- estimateSimpleSBM(adjacencyMatrix, 'poisson',
   estimOptions = list(plot = FALSE, nbCores = 1))
#> -> Estimation for 1 groups
#> 
-> Computation of eigen decomposition used for initalizations
#> -> Pass 1
#>     -> With ascending number of groups
#>         -> For 2 groups
#> 
        -> For 3 groups
#> 
        -> For 4 groups
#> 
        -> For 5 groups
#> 
    -> With descending number of groups
#>         -> For 4 groups
#> 

        -> For 3 groups
#> 
        -> For 2 groups
#> 
-> Pass 2
#>     -> With ascending number of groups
#>         -> For 2 groups
#>         -> For 3 groups
#>         -> For 4 groups
#>         -> For 5 groups
#>     -> With descending number of groups
#>         -> For 4 groups
#>         -> For 3 groups
#>         -> For 2 groups
plot(mySimpleSBM, 'data', ordered = FALSE)

plot(mySimpleSBM, 'data')

plot(mySimpleSBM, 'expected', ordered = FALSE)

plot(mySimpleSBM, 'expected')


### =======================================
### SIMPLE GAUSSIAN SBM

## Graph parameters & Sampling
nbNodes  <- 60
blockProp <- c(.5, .25, .25)      # group proportions
means <- diag(15., 3) + 5 # connectivity matrix: affiliation network
connectParam <- list(mean = means, var = 2)
mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam, model = "gaussian")

## Estimation
mySimpleSBM <-
   estimateSimpleSBM(mySampler$networkData, 'gaussian',
     estimOptions = list(plot = FALSE, nbCores = 1))
#> -> Estimation for 1 groups
#> 
-> Computation of eigen decomposition used for initalizations
#> -> Pass 1
#>     -> With ascending number of groups
#>         -> For 2 groups
#> 
        -> For 3 groups
#> 
        -> For 4 groups
#> 
        -> For 5 groups
#> 
    -> With descending number of groups
#>         -> For 4 groups
#> 

        -> For 3 groups
#> 
        -> For 2 groups
#> 
-> Pass 2
#>     -> With ascending number of groups
#>         -> For 2 groups
#>         -> For 3 groups
#>         -> For 4 groups
#>         -> For 5 groups
#>     -> With descending number of groups
#>         -> For 4 groups
#>         -> For 3 groups
#>         -> For 2 groups
plot(mySimpleSBM, 'data', ordered = FALSE)

plot(mySimpleSBM, 'data')

plot(mySimpleSBM, 'expected', ordered = FALSE)

plot(mySimpleSBM, 'expected')