Sbm() R function from [greed]

Stochastic Block Model Prior class

An S4 class to represent a Stochastic Block Model. Such model can be used to cluster graph vertex, and model a square adjacency matrix $X$ with the following generative model : [REMOVE_ME] $\pi \sim Dirichlet(\alpha) [REMOVE_ME_2]$

[REMOVE_ME] $Z_i \sim \mathcal{M}(1,\pi) [REMOVE_ME_2]$

[REMOVE_ME] $\theta_{kl} \sim Beta(a_0,b_0) [REMOVE_ME_2]$

[REMOVE_ME] $X_{ij}|Z_{ik}Z_{jl}=1 \sim \mathcal{B}(\theta_{kl}) [REMOVE_ME_2]$

These classes mainly store the prior parameters value $\alpha,a_0,b_0$ of this generative model. The Sbm-class must be used when fitting a simple Sbm whereas the SbmPrior-class must be used when fitting a CombinedModels-class. class


SbmPrior(a0 = 1, b0 = 1, type = "guess")

Sbm(alpha = 1, a0 = 1, b0 = 1, type = "guess")

Arguments

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", "undirected" or "guess", default to "guess"), for undirected graphs the adjacency matrix is supposed to be symmetric.
alpha: Dirichlet prior parameter over the cluster proportions (default to 1)

Returns

a SbmPrior-class object

a Sbm-class object

Description

An S4 class to represent a Stochastic Block Model. 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})

Examples


Sbm()
SbmPrior()
SbmPrior(type = "undirected")
Sbm()
Sbm(type = "undirected")

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

Sbm function