Stochastic Block Model with sampling scheme class

Source: R/misssbm.R

An S4 class to represent a Stochastic Block Model with a sampling scheme for missing data, extend icl_model-class. Such model can be used to cluster graph vertex, and model a square adjacency matrix \(X\) with the following generative model : $$ \pi \sim Dirichlet(\alpha)$$ $$ Z_i \sim \mathcal{M}(1,\pi)$$ $$ \theta_{kl} \sim Beta(a_0,b_0)$$ $$ X_{ij}|Z_{ik}Z_{jl}=1 \sim \mathcal{B}(\theta_{kl})$$ Missing value are supposed to be generated afterwards, the observation process correspond to a binary matrix \(R\) of the same size as \(X\), with \(R_{ij}=1\) for observed entries and \(R_{ij}=0\) for missing ones. \(R\) may be supposed to be MAR: $$ \epsilon \sim Beta(a_{0obs},b_{0obs})$$ $$ R_{ij} \sim \mathcal{B}(\epsilon)$$ this correspond to the "dyad" sampling scheme. But the sampling scheme can also be NMAR: $$ \epsilon_{kl} \sim Beta(a_{0obs},b_{0obs})$$ $$ R_{ij}|Z_{ik}Z_{jl}=1 \sim \mathcal{B}(\epsilon_{kl})$$ this correspond to the "block-dyad" sampling scheme. This class mainly store the prior parameters value \(\alpha,a_0,b_0,a_{0obs},b_{0obs}\) of this generative model in the following slots:

Slots

name

name of the model

alpha

Dirichlet over cluster proportions prior parameter (default to 1)

a0

Beta prior parameter over links (default to 1)

b0

Beta prior parameter over no-links (default to 1)

type

define the type of networks (either "directed" or "undirected", default to "directed")

sampling

define the sampling process (either "dyad" or "block-dyad" )

sampling_priors

define the sampling process priors parameters (list with a0obs and b0obs fields.)

References

Nowicki, Krzysztof and Tom A B Snijders (2001). “Estimation and prediction for stochastic block structures”. In:Journal of the American statistical association 96.455, pp. 1077–1087

See also

misssbm_fit-class,misssbm_path-class

greed

Examples

new("misssbm")

#> An object of class "misssbm"
#> Slot "sampling":
#> [1] "block-dyad"
#> 
#> Slot "sampling_priors":
#> $a0obs
#> [1] 1
#> 
#> $b0obs
#> [1] 1
#> 
#> 
#> Slot "a0":
#> [1] 1
#> 
#> Slot "b0":
#> [1] 1
#> 
#> Slot "type":
#> [1] "directed"
#> 
#> Slot "name":
#> [1] "misssbm"
#> 
#> Slot "alpha":
#> [1] 1
#> 
new("misssbm",a0=0.5, b0= 0.5,alpha=0.5,sampling="dyad",sampling_priors=list(a0obs = 2,b0obs = 1))

#> An object of class "misssbm"
#> Slot "sampling":
#> [1] "dyad"
#> 
#> Slot "sampling_priors":
#> $a0obs
#> [1] 2
#> 
#> $b0obs
#> [1] 1
#> 
#> 
#> Slot "a0":
#> [1] 0.5
#> 
#> Slot "b0":
#> [1] 0.5
#> 
#> Slot "type":
#> [1] "directed"
#> 
#> Slot "name":
#> [1] "misssbm"
#> 
#> Slot "alpha":
#> [1] 0.5
#> 
sbm = rsbm(100,c(0.5,0.5),diag(2)*0.1+0.01)
sbm$x[cbind(base::sample(1:100,50),base::sample(1:100,50))]=NA
sol = greed(sbm$x,model=new("misssbm",sampling="dyad"))

#> ------- directed MISSSBM with dyad sampling model fitting ------
#> ################# Generation  1: best solution with an ICL of -2419 and 2 clusters #################
#> ################# Generation  2: best solution with an ICL of -2419 and 2 clusters #################
#> ------- Final clustering -------
#> ICL clustering with a MISSSBM model, 2 clusters and an icl of -2419.