estimateMissSBM function

Estimation of simple SBMs with missing data

Variational EM inference of Stochastic Block Models indexed by block number from a partially observed network.

estimateMissSBM(
  adjacencyMatrix,
  vBlocks,
  sampling,
  covariates = list(),
  control = list()
)

Arguments

• adjacencyMatrix: The N x N adjacency matrix of the network data. If adjacencyMatrix is symmetric, we assume an undirected network with no loop; otherwise the network is assumed to be directed.

• vBlocks: The vector of number of blocks considered in the collection.

• sampling: The model used to described the process that originates the missing data: MAR designs ("dyad", "node","covar-dyad","covar-node","snowball") and MNAR designs ("double-standard", "block-dyad", "block-node" , "degree") are available. See details.

• covariates: An optional list with M entries (the M covariates). If the covariates are node-centered, each entry of covariates

  must be a size-N vector; if the covariates are dyad-centered, each entry of covariates must be N x N matrix.

• control: a list of parameters controlling advanced features. See details.

Returns

Returns an R6 object with class missSBM_collection.

Details

Internal functions use future_lapply, so set your plan to 'multisession' or 'multicore' to use several cores/workers. The list of parameters control tunes more advanced features, such as the initialization, how covariates are handled in the model, and the variational EM algorithm:

• useCov logical. If covariates is not null, should they be used for the for the SBM inference (or just for the sampling)? Default is TRUE.
• clusterInit Initial method for clustering: either a character ("spectral") or a list with length(vBlocks) vectors, each with size ncol(adjacencyMatrix), providing a user-defined clustering. Default is "spectral". similarity An R x R -> R function to compute similarities between node covariates. Default is l1_similarity, that is, -abs(x-y). Only relevant when the covariates are node-centered (i.e. covariates is a list of size-N vectors).
• threshold V-EM algorithm stops stop when an optimization step changes the objective function or the parameters by less than threshold. Default is 1e-2.
• maxIter V-EM algorithm stops when the number of iteration exceeds maxIter. Default is 50.
• fixPointIter number of fix-point iterations in the V-E step. Default is 3.
• exploration character indicating the kind of exploration used among "forward", "backward", "both" or "none". Default is "both".
• iterates integer for the number of iterations during exploration. Only relevant when exploration is different from "none". Default is 1.
• trace logical for verbosity. Default is TRUE.

The different sampling designs are split into two families in which we find dyad-centered and node-centered samplings. See tools:::Rd_expr_doi("10.1080/01621459.2018.1562934") for a complete description.

• Missing at Random (MAR)

  • dyad parameter = p = Prob(Dyad(i,j) is observed)
  • node parameter = p = Prob(Node i is observed)
  • covar-dyad": parameter = beta in R^M, such that Prob(Dyad (i,j) is observed) = logistic(parameter' covarArray (i,j, .))
  • covar-node": parameter = nu in R^M such that Prob(Node i is observed) = logistic(parameter' covarMatrix (i,)
  • snowball": parameter = number of waves with Prob(Node i is observed in the 1st wave)

• Missing Not At Random (MNAR)

  • double-standard parameter = (p0,p1) with p0 = Prob(Dyad (i,j) is observed | the dyad is equal to 0), p1 = Prob(Dyad (i,j) is observed | the dyad is equal to 1)
  • block-node parameter = c(p(1),...,p(Q)) and p(q) = Prob(Node i is observed | node i is in cluster q)
  • block-dyad parameter = c(p(1,1),...,p(Q,Q)) and p(q,l) = Prob(Edge (i,j) is observed | node i is in cluster q and node j is in cluster l)

Examples

## SBM parameters
N <- 100 # number of nodes
Q <- 3   # number of clusters
pi <- rep(1,Q)/Q     # block proportion
theta <- list(mean = diag(.45,Q) + .05 ) # connectivity matrix

## Sampling parameters
samplingParameters <- .75 # the sampling rate
sampling  <- "dyad"      # the sampling design

## generate a undirected binary SBM with no covariate
sbm <- sbm::sampleSimpleSBM(N, pi, theta)

## Uncomment to set parallel computing with future
## future::plan("multicore", workers = 2)

## Sample some dyads data + Infer SBM with missing data
collection <-
   observeNetwork(sbm$networkData, sampling, samplingParameters) %>%
   estimateMissSBM(vBlocks = 1:4, sampling = sampling)
plot(collection, "monitoring")
plot(collection, "icl")

collection$ICL
coef(collection$bestModel$fittedSBM, "connectivity")

myModel <- collection$bestModel
plot(myModel, "expected")
plot(myModel, "imputed")
plot(myModel, "meso")
coef(myModel, "sampling")
coef(myModel, "connectivity")
predict(myModel)[1:5, 1:5]

See Also

observeNetwork, missSBM_collection and missSBM_fit.