An R6 class to represent an SBM fit with missing data

The function estimateMissSBM() fits a collection of SBM for varying number of block. Each fitted SBM is an instance of an R6 object with class missSBM_fit, described here.

Fields are accessed via active binding and cannot be changed by the user.

This class comes with a set of R6 methods, some of them being useful for the user and exported as S3 methods. See the documentation for show(), print(), fitted(), predict(), plot().

Active bindings

fittedSBM: the fitted SBM with class SimpleSBM_fit_noCov, SimpleSBM_fit_withCov or SimpleSBM_fit_MNAR inheriting from class sbm::SimpleSBM_fit
fittedSampling: the fitted sampling, inheriting from class networkSampling and corresponding fits
imputedNetwork: The network data as a matrix with NAs values imputed with the current model
monitoring: a list carrying information about the optimization process
occupiedBlocks: the number of classes actually occupied by at least one node; can be less than fittedSBM$nbBlocks for an over-specified fit whose VEM has collapsed one or more classes (see repair())
degenerate: TRUE if occupiedBlocks < fittedSBM$nbBlocks
entropyImputed: the entropy of the distribution of the imputed dyads
entropy: the entropy due to the distribution of the imputed dyads and of the clustering
vExpec: double: variational expectation of the complete log-likelihood
penalty: double, value of the penalty term in ICL
loglik: double: approximation of the log-likelihood (variational lower bound) reached
ICL: double: value of the integrated classification log-likelihood

Methods

`missSBM_fit$new()`

constructor for networkSampling

Usage

missSBM_fit$new(partlyObservedNet, netSampling, clusterInit, useCov = TRUE)

Arguments

partlyObservedNet: An object with class partlyObservedNetwork.
netSampling: The sampling design for the modelling of missing data: MAR designs ("dyad", "node") and MNAR designs ("double-standard", "block-dyad", "block-node" ,"degree")
clusterInit: Initial clustering: a vector with size ncol(adjacencyMatrix), providing a user-defined clustering. The number of blocks is deduced from the number of levels in with clusterInit.
useCov: logical. If covariates are present in partlyObservedNet, should they be used for the inference or of the network sampling design, or just for the SBM inference? default is TRUE.

`missSBM_fit$doVEM()`

a method to perform inference of the current missSBM fit with variational EM

Usage

missSBM_fit$doVEM(
  control = list(threshold = 0.01, maxIter = 100, fixPointIter = 3, trace = TRUE)
)

Arguments

control: a list of VEM control parameters (see estimateMissSBM())

`missSBM_fit$split()`

clone of the current fit after splitting cluster index in two, via a spectral bipartition of the sub-network it induces. Builds but does not fit the candidate (see candidates_split()).

Usage

missSBM_fit$split(index, in_place = FALSE, base_net = NULL)

Arguments

index: index (integer) of the cluster to split
in_place: replace self's own fit (TRUE) or return a new object (FALSE, the default)?
base_net: optional precomputed network to bipartition (as built internally at the top of this method); lets candidates_split() avoid recomputing it once per candidate.

Returns

a new missSBM_fit with one more block, or NULL if index cannot be split (its induced sub-network has zero variance)

`missSBM_fit$candidates_split()`

generate and cheaply trial-fit candidates obtained by splitting each splittable cluster in two (see split()). A cluster is splittable if it has at least 4 members and non-zero variance in its induced sub-network.

Usage

missSBM_fit$candidates_split(
  control = list(threshold = 0.01, maxIter = 100, fixPointIter = 3, trace = TRUE),
  trial_niter = 2
)

Arguments

control: a list of VEM control parameters (see estimateMissSBM()); maxIter is overridden by trial_niter
trial_niter: number of VEM iterations used for the trial fits. Default is 2.

Returns

a list of trial-fitted missSBM_fit candidates (one per splittable cluster)

`missSBM_fit$merge()`

clone of the current fit after merging clusters indices[1] and indices[2] into one. Builds but does not fit the candidate (see candidates_merge()).

Usage

missSBM_fit$merge(indices, in_place = FALSE)

Arguments

indices: indices (couple of integers) of the clusters to merge
in_place: replace self's own fit (TRUE) or return a new object (FALSE, the default)?

Returns

a new missSBM_fit with one fewer block

`missSBM_fit$candidates_merge()`

generate and cheaply trial-fit candidates obtained by merging pairs of clusters (see merge()). Beyond max_candidates pairs (quadratic in the number of blocks), only the most similar-connectivity pairs are tried.

Usage

missSBM_fit$candidates_merge(
  control = list(threshold = 0.01, maxIter = 100, fixPointIter = 3, trace = TRUE),
  max_candidates = 30,
  trial_niter = 2
)

Arguments

control: a list of VEM control parameters (see estimateMissSBM()); maxIter is overridden by trial_niter
max_candidates: cap on the number of pairs tried. Default is 30.
trial_niter: number of VEM iterations used for the trial fits. Default is 2.

Returns

a list of trial-fitted missSBM_fit candidates

`missSBM_fit$repair()`

recovers a degenerate fit (fewer occupied classes than its structural nbBlocks, e.g. after a VEM component collapse) by filling the empty classes (see repair_empty_classes()) and refitting the full VEM. Mutates self in place; a no-op if the fit is not degenerate.

Usage

missSBM_fit$repair(
  control = list(threshold = 0.01, maxIter = 100, fixPointIter = 3, trace = TRUE)
)

Arguments

control: a list of VEM control parameters (see estimateMissSBM())

Returns

invisibly, self

`missSBM_fit$polish()`

discrete node-swap polishing (Kernighan-Lin / greedy-ICL style): after VEM convergence, tau is near-hard and its fixed point cannot relocate a single misclassified node (only split()/merge() fix group-level mistakes). Each sweep computes, for every node, the closed-form complete-data log-likelihood gain of moving it to its best alternative class (theta/pi held fixed), applies the improving, non-class-emptying moves, then runs a full VEM to resettle. Stops as soon as a sweep fails to improve the ICL, mutates self in place, and never leaves the ICL worse than before the call.

Usage

missSBM_fit$polish(
  control = list(threshold = 0.01, maxIter = 100, fixPointIter = 3, trace = TRUE),
  max_sweeps = 10
)

Arguments

control: a list of VEM control parameters (see estimateMissSBM())
max_sweeps: maximum number of swap sweeps. Default is 10.

Returns

invisibly, self

`missSBM_fit$show()`

show method for missSBM_fit

Usage

missSBM_fit$show()

`missSBM_fit$print()`

User friendly print method

Usage

missSBM_fit$print()

`missSBM_fit$clone()`

The objects of this class are cloneable with this method.

Usage

missSBM_fit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

## Sample 75% of dyads in  French political Blogosphere's network data
adjMatrix <- missSBM::frenchblog2007 %>%
  igraph::as_adjacency_matrix(sparse = FALSE) %>%
  missSBM::observeNetwork(sampling = "dyad", parameters = 0.75)
collection <- estimateMissSBM(adjMatrix, 3:5, sampling = "dyad")
#> 
#> 
#>  Adjusting Variational EM for Stochastic Block Model
#> 
#> 	Imputation assumes a 'dyad' network-sampling process
#> 
#>  Initialization of 3 model(s). 
#>  Performing VEM inference
#>  	Model with 3 blocks.
 	Model with 4 blocks.
 	Model with 5 blocks.
 Polishing (node-swap)
#> 
#>  Looking for better solutions
#>  Pass 1   Going forward ++
                                                                                                    
 Pass 1   Going backward ++
                                                                                                    

my_missSBM_fit <- collection$bestModel
class(my_missSBM_fit)
#> [1] "missSBM_fit" "R6"         
plot(my_missSBM_fit, "imputed")