BDgraph (version 2.74)

bdgraph: Search algorithm in graphical models

Description

As the main function of the BDgraph package, this function consists of several MCMC sampling algorithms for Bayesian model determination in undirected graphical models. To speed up the computations, the birth-death MCMC sampling algorithms are implemented in parallel using OpenMP in C++.

Usage

bdgraph(data, n = NULL, method = "ggm", algorithm = "bdmcmc", iter = 5000, 
        burnin = iter / 2, not.cont = NULL, g.prior = 0.2, df.prior = 3, 
        g.start = "empty", jump = NULL, save = FALSE, 
        cores = NULL, threshold = 1e-8, verbose = TRUE, nu = 1)

Value

An object with S3 class "bdgraph" is returned:

p_links

upper triangular matrix which corresponds the estimated posterior probabilities of all possible links.

K_hat

posterior estimation of the precision matrix.

For the case "save = TRUE" is returned:

sample_graphs

vector of strings which includes the adjacency matrices of visited graphs after burn-in.

graph_weights

vector which includes the waiting times of visited graphs after burn-in.

all_graphs

vector which includes the identity of the adjacency matrices for all iterations after burn-in. It is needed for monitoring the convergence of the BD-MCMC algorithm.

all_weights

vector which includes the waiting times for all iterations after burn-in. It is needed for monitoring the convergence of the BD-MCMC algorithm.

Arguments

data

there are two options: (1) an (\(n \times p\)) matrix or a data.frame corresponding to the data, (2) an (\(p \times p\)) covariance matrix as \(S=X'X\) which \(X\) is the data matrix (\(n\) is the sample size and \(p\) is the number of variables). It also could be an object of class "sim", from function bdgraph.sim. The input matrix is automatically identified by checking the symmetry.

n

number of observations. It is needed if the "data" is a covariance matrix.

method

character with two options "ggm" (default) and "gcgm". Option "ggm" is for Gaussian graphical models based on Gaussianity assumption. Option "gcgm" is for Gaussian copula graphical models for the data that not follow Gaussianity assumption (e.g. continuous non-Gaussian, count, or mixed dataset).

algorithm

character with two options "bdmcmc" (default) and "rjmcmc". Option "bdmcmc" is based on birth-death MCMC algorithm. Option "rjmcmc" is based on reverible jump MCMC algorithm. Option "bd-dmh" is based on birth-death MCMC algorithm using double Metropolis Hasting. Option "rj-dmh" is based on reverible jump MCMC algorithm using double Metropolis Hasting.

iter

number of iteration for the sampling algorithm.

burnin

number of burn-in iteration for the sampling algorithm.

not.cont

for the case method = "gcgm", a vector with binary values in which \(1\) indicates not continuous variables.

g.prior

for determining the prior distribution of each edge in the graph. There are two options: a single value between \(0\) and \(1\) (e.g. \(0.5\) as a noninformative prior) or an (\(p \times p\)) matrix with elements between \(0\) and \(1\).

df.prior

degree of freedom for G-Wishart distribution, \(W_G(b,D)\), which is a prior distribution of the precision matrix.

g.start

corresponds to a starting point of the graph. It could be an (\(p \times p\)) matrix, "empty" (default), or "full". Option "empty" means the initial graph is an empty graph and "full" means a full graph. It also could be an object with S3 class "bdgraph" of R package BDgraph or the class "ssgraph" of R package ssgraph::ssgraph(); this option can be used to run the sampling algorithm from the last objects of previous run (see examples).

jump

it is only for the BDMCMC algorithm (algorithm = "bdmcmc"). It is for simultaneously updating multiple links at the same time to update graph in the BDMCMC algorithm.

save

logical: if FALSE (default), the adjacency matrices are NOT saved. If TRUE, the adjacency matrices after burn-in are saved.

cores

number of cores to use for parallel execution. The case cores = "all" means all CPU cores to use for parallel execution.

threshold

threshold value for the convergence of sampling algorithm from G-Wishart for the precision matrix.

verbose

logical: if TRUE (default), report/print the MCMC running time.

nu

prior parameter for option method = "tgm".

Author

Reza Mohammadi and Ernst Wit

References

Mohammadi, R. and Wit, E. C. (2019). BDgraph: An R Package for Bayesian Structure Learning in Graphical Models, Journal of Statistical Software, 89(3):1-30, tools:::Rd_expr_doi("10.18637/jss.v089.i03")

Mohammadi, A. and Wit, E. C. (2015). Bayesian Structure Learning in Sparse Gaussian Graphical Models, Bayesian Analysis, 10(1):109-138, tools:::Rd_expr_doi("10.1214/14-BA889")

Mohammadi, R., Massam, H. and Letac, G. (2023). Accelerating Bayesian Structure Learning in Sparse Gaussian Graphical Models, Journal of the American Statistical Association, tools:::Rd_expr_doi("10.1080/01621459.2021.1996377")

Mohammadi, A. et al (2017). Bayesian modelling of Dupuytren disease by using Gaussian copula graphical models, Journal of the Royal Statistical Society: Series C, 66(3):629-645, tools:::Rd_expr_doi("10.1111/rssc.12171")

Dobra, A. and Mohammadi, R. (2018). Loglinear Model Selection and Human Mobility, Annals of Applied Statistics, 12(2):815-845, tools:::Rd_expr_doi("10.1214/18-AOAS1164")

Vogels, L., Mohammadi, R., Schoonhoven, M., and Birbil, S.I. (2024) Bayesian Structure Learning in Undirected Gaussian Graphical Models: Literature Review with Empirical Comparison, Journal of the American Statistical Association, tools:::Rd_expr_doi("10.1080/01621459.2024.2395504")

Mohammadi, R., Schoonhoven, M., Vogels, L., and Birbil, S.I. (2023) Scalable Bayesian Structure Learning for Gaussian Graphical Models Using Marginal Pseudo-likelihood, arXiv preprint, tools:::Rd_expr_doi("10.48550/arXiv.2307.00127")

Mohammadi, A. and Dobra A. (2017). The R Package BDgraph for Bayesian Structure Learning in Graphical Models, ISBA Bulletin, 24(4):11-16

See Also

bdgraph.mpl, bdgraph.dw, bdgraph.sim, summary.bdgraph, compare

Examples

if (FALSE) {
set.seed(10)

# - - Example 1

# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim(n = 100, p = 10, size = 15, vis = TRUE)
   
bdgraph.obj <- bdgraph(data = data.sim, iter = 1000, save = TRUE)
  
summary(bdgraph.obj)

# Confusion Matrix
conf.mat(actual = data.sim, pred = bdgraph.obj)

conf.mat.plot(actual = data.sim, pred = bdgraph.obj)
   
# To compare our result with true graph
compare(bdgraph.obj, data.sim, main = c("Target", "BDgraph"), vis = T)

# Running algorithm with starting points from previous run
bdgraph.obj2 <- bdgraph(data = data.sim, g.start = bdgraph.obj)
    
compare(list(bdgraph.obj, bdgraph.obj2), data.sim, 
        main = c("Target", "Frist run", "Second run"))

# - - Example 2

# Generating mixed data from a 'scale-free' graph
data.sim <- bdgraph.sim(n = 200, p = 7, type = "mixed", graph = "scale-free", vis = TRUE)
   
bdgraph.obj <- bdgraph(data = data.sim, method = "gcgm")
  
summary(bdgraph.obj)
   
compare(bdgraph.obj, data.sim, vis = T)

conf.mat(actual = data.sim, pred = bdgraph.obj)

conf.mat.plot(actual = data.sim, pred = bdgraph.obj)
}