noisysbmGGM: Noisy Stochastic Block Mode: Graph and GGM Inference by Multiple Testing and Greedy Bayesian Algorithm

Description

Greedy Bayesian algorithm to fit the noisy stochastic block model to an observed sparse graph. Moreover, a graph inference procedure to recover Gaussian Graphical Model from real data. This procedure comes with a control of the false discovery rate. The method is described in the article "Enhancing the Power of Gaussian Graphical Model Inference by Modeling the Graph Structure" by Kilian, Rebafka, and Villers (2024) arXiv:2402.19021.

Author(s)

Maintainer: Valentin Kilian valentin.kilian@ens-rennes.fr

Authors:

• Fanny Villers fanny.villers@upmc.fr

Evalute the adjusted Rand index

Description

Compute the adjusted Rand index to compare two partitions

Usage

ARI(x, y)

Arguments

Details

the partitions may be provided as n-vectors containing the cluster memeberships of n entities, or by Qxn - matrices whose entries are all 0 and 1 where 1 indicates the cluster membership

Value

the value of the adjusted Rand index

Examples

clust1 <- c(1,2,1,2)
clust2 <- c(2,1,2,1)
ARI(clust1, clust2)

clust3 <- matrix(c(1,1,0,0, 0,0,1,1), nrow=2, byrow=TRUE)
clust4 <- matrix(c(1,0,0,0, 0,1,0,0, 0,0,1,1), nrow=3, byrow=TRUE)
ARI(clust3, clust4)

GGM for test

Description

Example of a GGM

Usage

GGMtest

Format

dataMatrix

A n-sample of a p Gaussian Vector associated to a GGM G

Z.true

True latent clustering

A.true

True latent adjacency matrix of the graph G

Examples

main_noisySBM_GGM(GGMtest$dataMatrix,Meth="Ren",NIG=TRUE,Qup=10,nbOfZ=1,nbCores=1)

#Note : These data were created using the following instructions
n=30
p=10
u=0.1
v=0.3
theta=list(pi=c(1/3,2/3),w=0.25*cbind(c(1/6,1/120),c(1/120,1/6)))
Q=2
Z <- sample(1:Q, p, replace=TRUE, prob=theta$pi)
A <- matrix(0, p, p)
for (i in 1:(p-1)){
    A[i,(i+1):p] <- stats::rbinom(p-i, 1, theta$w[Z[i],Z[(i+1):p]])}
 A.true <- A + t(A)
Omega <- A.true*v
diag(Omega) = abs(min(eigen(Omega)$values)) + 0.1 + u
Sigma = stats::cov2cor(solve(Omega))
X = MASS::mvrnorm(n, rep(0, p), Sigma)
GGMtest=list(dataMatrix=X,Z.true=Z,A.true=A.true)

NoisySBM for test

Description

Example of NoisySBM data

Usage

NSBMtest

Format

dataMatrix

A square matrix containing the observation of the graph

theta

True NSBM parameters

latentZ

True latent clustering

latentAdj

True latent adjacency matrix

Examples

main_noisySBM(NSBMtest$dataMatrix,NIG=TRUE,Qup=10,nbOfZ=1,nbCores=1)

#Note : These data were created using the following instructions
p=50
Q=6
pi=c(1/6,1/6,1/6,1/6,1/6,1/6)
w=c(0.811,0.001,0.001,0.001,0.001,0.001,0.811,0.011,0.001,0.001,0.001,
0.811,0.001,0.001,0.001,0.811,0.001,0.001,0.811,0.011,0.811)
theta=list(pi=pi,w=w,nu0=c(0,1))
theta$nu <- array(0, dim = c(Q*(Q+1)/2, 2))
theta$nu[,1] <- rep(2,21)
theta$nu[,2] <- rep(2,21)
NSBMtest=rnsbm(p,theta)

Graph Inference from Noisy Data by Multiple Testing

Description

The main_noisySBM() function is a core component of the noisysbmGGM package, responsible for applying the greedy algorithm to estimate model parameters, perform node clustering, and conduct a multiple testing procedure to infer the underlying graph. This function is versatile, offering various options and providing useful outputs for further analysis

Usage

main_noisySBM(
  X,
  NIG = FALSE,
  threshold = 0.5,
  Nbrepet = 2,
  rho = NULL,
  tau = NULL,
  a = NULL,
  b = NULL,
  c = NULL,
  d = NULL,
  n0 = 1,
  eta0 = 1,
  zeta0 = 1,
  alpha = 0.1,
  Qup = NULL,
  nbCores = parallel::detectCores(),
  nbOfZ = 12,
  sigma0 = 1,
  sigma1 = 1,
  percentageOfPerturbation = 0.3,
  verbatim = TRUE
)

Arguments

Value

Examples

main_noisySBM(NSBMtest$dataMatrix,NIG=TRUE,Qup=10,nbOfZ=1,nbCores=1)

GGM Inference from Noisy Data by Multiple Testing using SILGGM and Drton test statistics

Description

The main_noisySBM_GGM() function is a key feature of the noisysbmGGM package, dedicated to Gaussian Graphical Model (GGM) inference. This function takes an $n$-sample of a Gaussian vector of dimension $p$ and provides the GGM associated with the partial correlation structure of the vector. GGM inference is essential in capturing the underlying relationships between the vector's coefficients, helping users uncover meaningful interactions while controlling the number of false discoveries.

Usage

main_noisySBM_GGM(
  X,
  Meth = "Ren",
  NIG = NULL,
  threshold = 0.5,
  Nbrepet = 2,
  rho = NULL,
  tau = NULL,
  a = NULL,
  b = NULL,
  c = NULL,
  d = NULL,
  n0 = 1,
  eta0 = 1,
  zeta0 = 1,
  alpha = 0.1,
  Qup = NULL,
  nbCores = parallel::detectCores(),
  nbOfZ = 12,
  sigma0 = 1,
  sigma1 = 1,
  percentageOfPerturbation = 0.3,
  verbatim = TRUE
)

Arguments

Value

#' @examples main_noisySBM_GGM(GGMtest$dataMatrix,Meth="Ren",NIG=TRUE,Qup=10,nbOfZ=1)

See Also

main_noisySBM

matrixToVec

Description

matrixToVec

Usage

matrixToVec(X)

Arguments

Value

a vector contenting the coefficient of the upper triangle of the matrix X from left to right and from top to bottom.

plot the data matrix, the inferred graph and/or the true binary graph

Description

plot the data matrix, the inferred graph and/or the true binary graph

Usage

plotGraphs(dataMatrix = NULL, inferredGraph = NULL, binaryTruth = NULL)

Arguments

Value

a list of FDR and TDR values, if possible

return a random NSBM

Description

return a random NSBM

Usage

rnsbm(p, theta, modelFamily = "Gauss")

Arguments

Value

X the noisy matrix

theta

latentZ the latent clustering

latentA the latent adjacency matrix latent variables we strat by sampling the latent variable Z which is the vector containing the family of each nodes adjacency matrix then we sample the adjacency matrix, conditionally to Z the coordinate of A follow a binomial of a parameter contain in theta$w noisy observations under the null we create a matrix (n,n) X and we initialize all its entry (half of them is undirected) with a sampling of the law under the null then for each entry where A is none zero we sample it according to the law under the alternative

vecToMatrix

Description

vecToMatrix

Usage

vecToMatrix(X, p)

Arguments

Value

a p by p symetric matrix whose upper triangle coefficients from left to right and from top to bottom are the entries of the vector X