estimateMissSBM {missSBM}

Estimation of simple SBMs with missing data

Description

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

Usage

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.

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 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)

Value

Returns an R6 object with class missSBM_collection.

See Also

observeNetwork, missSBM_collection and missSBM_fit.

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]