estimateBipartiteSBM function

Estimation of Bipartite SBMs

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

estimateBipartiteSBM(
  netMat,
  model = "bernoulli",
  dimLabels = c(row = "row", col = "col"),
  covariates = list(),
  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.
• estimOptions: a list of parameters controlling the inference algorithm and model selection. See details.

Returns

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
• "verbosity" integer for verbosity (0, 1). Default is 1
• "plot" boolean, should the ICL by dynamically plotted or not. Default is TRUE
• "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

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))
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))
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))
plot(myBipartiteSBM, 'expected')