Estimation of Bipartite SBMs — estimateBipartiteSBM • sbm

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

Usage

estimateBipartiteSBM(
  netMat,
  model = "bernoulli",
  dimLabels = c(row = "row", col = "col"),
  covariates = list(),
  nodesCovariates = vector("list", 2),
  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'.
dimLabels: an optional vector of labels for each dimension (in row, in column)
covariates: a list of matrices with same dimension as mat describing covariates at the edge level. No covariate per Default.
nodesCovariates: a list of two matrices with the same number of rows as the number of nodes in rows and cols in the network, describing the nodes covariates for each type of nodes. 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

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

## Graph parameters and Sampling
nbNodes <- c(60, 80)
blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions
means <- matrix(runif(6), 2, 3)  # connectivity matrix
# In Bernoulli SBM, parameters is a list with a
# matrix of means 'mean' which are probabilities of connection
connectParam <- list(mean = means)
mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'bernoulli')

## Estimation
myBipartiteSBM <- estimateBipartiteSBM(mySampler$networkData,
  estimOptions = list(plot = FALSE, nbCores = 1))
#> -> Estimation for 2 groups (1+1)
#> 
-> Computation of eigen decomposition used for initalizations
#>     -> for rows
#>     -> for cols
#> -> Pass 1
#>     -> With ascending number of groups
#>         -> For 3 groups
#> 
        -> For 4 groups
#> 
        -> For 5 groups
#> 
        -> For 6 groups
#> 
        -> For 7 groups
#> 

        -> For 8 groups
#> 

    -> With descending number of groups
#>         -> For 7 groups
#> 

        -> For 6 groups
#> 

        -> For 5 groups
#> 
        -> For 4 groups
#> 
        -> For 3 groups
#> 
-> Pass 2
#>     -> With ascending number of groups
#>         -> For 3 groups
#>         -> For 4 groups
#>         -> For 5 groups
#>         -> For 6 groups
#>         -> For 7 groups
#> 
        -> For 8 groups
#> 
    -> With descending number of groups
#>         -> For 7 groups
#>         -> For 6 groups
#>         -> For 5 groups
#>         -> For 4 groups
#>         -> For 3 groups
plot(myBipartiteSBM, 'expected')


### =======================================
### BIPARTITE POISSON SBM

## Graph parameters & Sampling
nbNodes <- c(60, 80)
blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions
means <- matrix(rbinom(6, 30, 0.25), 2, 3)  # connectivity matrix
connectParam <- list(mean = means)
mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'poisson')

## Estimation
myBipartiteSBM <-
  estimateBipartiteSBM(mySampler$networkData, 'poisson',
    estimOptions = list(plot = FALSE, nbCores = 1))
#> -> Estimation for 2 groups (1+1)
#> 
-> Computation of eigen decomposition used for initalizations
#>     -> for rows
#>     -> for cols
#> -> Pass 1
#>     -> With ascending number of groups
#>         -> For 3 groups
#> 
        -> For 4 groups
#> 
        -> For 5 groups
#> 
        -> For 6 groups
#> 
        -> For 7 groups
#> 

        -> For 8 groups
#> 

    -> With descending number of groups
#>         -> For 7 groups
#> 
        -> For 6 groups
#> 

        -> For 5 groups
#> 
        -> For 4 groups
#> 
        -> For 3 groups
#> 
-> Pass 2
#>     -> With ascending number of groups
#>         -> For 3 groups
#>         -> For 4 groups
#>         -> For 5 groups
#>         -> For 6 groups
#>         -> For 7 groups
#>         -> For 8 groups
#>     -> With descending number of groups
#>         -> For 7 groups
#>         -> For 6 groups
#>         -> For 5 groups
#>         -> For 4 groups
#>         -> For 3 groups
plot(myBipartiteSBM, 'expected')


### =======================================
### BIPARTITE GAUSSIAN SBM
## Graph parameters & sampling
nbNodes <- c(60, 80)
blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions
means <- 20 * matrix(runif(6), 2, 3)  # connectivity matrix
connectParam <- list(mean = means, var = 1)
mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'gaussian')

## Estimation
myBipartiteSBM <-
  estimateBipartiteSBM(mySampler$networkData, 'gaussian',
    estimOptions = list(plot = FALSE, nbCores = 1))
#> -> Estimation for 2 groups (1+1)
#> 
-> Computation of eigen decomposition used for initalizations
#>     -> for rows
#>     -> for cols
#> -> Pass 1
#>     -> With ascending number of groups
#>         -> For 3 groups
#> 
        -> For 4 groups
#> 
        -> For 5 groups
#> 
        -> For 6 groups
#> 
        -> For 7 groups
#> 

        -> For 8 groups
#> 

    -> With descending number of groups
#>         -> For 7 groups
#> 

        -> For 6 groups
#> 
        -> For 5 groups
#> 
        -> For 4 groups
#> 
        -> For 3 groups
#> 
-> Pass 2
#>     -> With ascending number of groups
#>         -> For 3 groups
#>         -> For 4 groups
#>         -> For 5 groups
#>         -> For 6 groups
#>         -> For 7 groups
#>         -> For 8 groups
#>     -> With descending number of groups
#>         -> For 7 groups
#>         -> For 6 groups
#>         -> For 5 groups
#>         -> For 4 groups
#>         -> For 3 groups
plot(myBipartiteSBM, 'expected')