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Estimation of simple SBMs with missing data

Source: R/estimateMissSBM.R
estimateMissSBM.Rd

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

Usage

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

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-like structure for controlling advanced features, with default generated by missSBM_param. See the associated documentation for details.

Value

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 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)

See also

observeNetwork, missSBM_collection, missSBM_fit and missSBM_param.

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)
#> 
#> 
#>  Adjusting Variational EM for Stochastic Block Model
#> 
#> 	Imputation assumes a 'dyad' network-sampling process
#> 
#>  Initialization of 4 model(s). 
#>  Performing VEM inference
#>  	Model with 3 blocks.
 	Model with 1 blocks.
 	Model with 4 blocks.
 	Model with 2 blocks.
 Polishing (node-swap)
#> 
#>  Looking for better solutions
#>  Pass 1   Going forward +++
                                                                                                    
 Pass 1   Going backward +++
                                                                                                    

plot(collection, "monitoring")

plot(collection, "icl")


collection$ICL
#> [1] 10584.442  9886.688  9485.626  9535.876
coef(collection$bestModel$fittedSBM, "connectivity")
#> $mean
#>            [,1]       [,2]       [,3]
#> [1,] 0.50247919 0.05509355 0.05696972
#> [2,] 0.05509355 0.50953677 0.05164995
#> [3,] 0.05696972 0.05164995 0.53003541
#> 

myModel <- collection$bestModel
plot(myModel, "expected")
#> Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
#> ℹ Please use tidy evaluation idioms with `aes()`.
#> ℹ See also `vignette("ggplot2-in-packages")` for more information.
#> ℹ The deprecated feature was likely used in the sbm package.
#>   Please report the issue at <https://github.com/GrossSBM/sbm/issues>.
#> Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
#> ℹ Please use `linewidth` instead.
#> ℹ The deprecated feature was likely used in the sbm package.
#>   Please report the issue at <https://github.com/GrossSBM/sbm/issues>.

plot(myModel, "imputed")

plot(myModel, "meso")

coef(myModel, "sampling")
#> [1] 0.7553535
coef(myModel, "connectivity")
#> $mean
#>            [,1]       [,2]       [,3]
#> [1,] 0.50247919 0.05509355 0.05696972
#> [2,] 0.05509355 0.50953677 0.05164995
#> [3,] 0.05696972 0.05164995 0.53003541
#> 
predict(myModel)[1:5, 1:5]
#> 5 x 5 sparse Matrix of class "dgCMatrix"
#>                                                   
#> [1,] .          . 0.05164995 .          .         
#> [2,] .          . 1.00000000 1.00000000 .         
#> [3,] 0.05164995 1 .          1.00000000 .         
#> [4,] .          1 1.00000000 .          0.05509355
#> [5,] .          . .          0.05509355 .