Estimate Parameters in the Generalized SBM

Given an adjacency matrix drawn from a Generalized Stochastic Block Model with missing observations, this package robustly estimates the probabilities of connection between nodes and detects outliers nodes, as describes in Gaucher, Klopp and Robin (2019) .

gsbm

This package implements the algorithm described in Gaucher et al. (2019). It fits a Generalized Stochastic Block Model to an unweighted, undirected adjacency matrix with missing observations, and estimate the probabilities of connection between nodes while detecting outliers.

Installation

You can install the released version of gsbm from CRAN with:

install.packages("gsbm")

Example

In this example, we simulated an adjacency matrix from a Generalized Stochastic Block Model. We then use to estimate the parameters of the model and detect outliers.

library(gsbm)

# We draw a 50x50 adjacency matrix from a generalized SBM with 2 communities and 2 outliers
# First, we create the low-rank matrix L
L <- matrix(0,50,50) # low-rank component
L[1:25, 1:25] <- 0.6 # connection probabilities within community 1
L[1:25, 26:48] <- 0.1 # connection probabilities between communities 1 and 2
L[26:48, 1:25] <- 0.1 # connection probabilities between communities 1 and 2
L[26:48, 26:48] <- 0.6 # connection probabilities within community 2

# Then , we create column-sparse matrix S
S <- matrix(0,50,50) # column sparse component
S[49:50,1:48] <- 0.6 # connection probabilties between outliers and inliers

# Finally, we draw the connections and create the adjacency matrix
undir <- rbinom(n=50*(50-1)/2, size=1, prob=(L+S+t(S))[upper.tri(L+S+t(S))]) 
A <- matrix(0,50,50)
A[upper.tri(A)] <- undir
A <- (A+t(A))

# We estimate the probabilities of connection using gsbm_mcgd
lambda1 <- 7
lambda2 <- 7
res <- gsbm_mcgd(A, lambda1, lambda2)
#> [1] "iter  10 : error  2.77460205956567e-06  - objective:  394.816716468949"