| Title: | Bayesian Structure Learning in Graphical Models using Birth-Death MCMC |
| Version: | 2.73 |
| Description: | Advanced statistical tools for Bayesian structure learning in undirected graphical models, accommodating continuous, ordinal, discrete, count, and mixed data. It integrates recent advancements in Bayesian graphical models as presented in the literature, including the works of Mohammadi and Wit (2015) <doi:10.1214/14-BA889>, Mohammadi et al. (2021) <doi:10.1080/01621459.2021.1996377>, Dobra and Mohammadi (2018) <doi:10.1214/18-AOAS1164>, and Mohammadi et al. (2023) <doi:10.48550/arXiv.2307.00127>. |
| URL: | https://www.uva.nl/profile/a.mohammadi |
| Imports: | igraph, ggplot2, pROC |
| Suggests: | ssgraph, huge, tmvtnorm, skimr, knitr, rmarkdown |
| VignetteBuilder: | knitr |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Repository: | CRAN |
| NeedsCompilation: | yes |
| Author: | Reza Mohammadi 
[aut, cre],
Ernst Wit [aut],
Adrian Dobra
[ctb] |
| Maintainer: | Reza Mohammadi <a.mohammadi@uva.nl> |
| Packaged: | 2024-08-23 12:43:58 UTC; a.mohammadiuva.nl |
| Date/Publication: | 2024-08-23 13:20:02 UTC |
Bayesian Structure Learning in Graphical Models
Description
The R package BDgraph provides statistical tools for Bayesian structure learning in undirected graphical models for continuous, ordinal/count/dicrete, binary, and mixed data. The package is implemented the recent improvements in the Bayesian graphical models' literature, including Mohammadi and Wit (2015), Mohammadi et al. (2023), Mohammadi et al. (2017), and Dobra and Mohammadi (2018). To speed up the computations, the intensive tasks of the package are implemented in parallel using OpenMP in C++ and interfaced with R. Besides, the package contains several functions for simulation and visualization, as well as several multivariate datasets taken from the literature.
How to cite this package
To cite BDgraph in publications use:
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, doi:10.18637/jss.v089.i03
Author(s)
Reza Mohammadi [aut, cre] (<https://orcid.org/0000-0001-9538-0648>),
Ernst Wit [aut] (<https://orcid.org/0000-0002-3671-9610>),
Adrian Dobra [ctb] (<https://orcid.org/0000-0001-7793-2197>).
Maintainer: Reza Mohammadi a.mohammadi@uva.nl
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, 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, 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, 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, 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, doi:10.1214/18-AOAS1164
Vogels, L., Mohammadi, R., Schoonhoven, M., and Birbil, S.I. (2023) Bayesian Structure Learning in Undirected Gaussian Graphical Models: Literature Review with Empirical Comparison, arXiv preprint, doi:10.48550/arXiv.2307.02603
Mohammadi, R., Schoonhoven, M., Vogels, L., and Birbil, S.I. (2023) Large-scale Bayesian Structure Learning for Gaussian Graphical Models using Marginal Pseudo-likelihood, arXiv preprint, doi:10.48550/arXiv.2307.00127
Vinciotti, V., Behrouzi, P., and Mohammadi, R. (2022) Bayesian structural learning of microbiota systems from count metagenomic data, arXiv preprint, doi:10.48550/arXiv.2203.10118
Dobra, A. and Lenkoski, A. (2011). Copula Gaussian graphical models and their application to modeling functional disability data, The Annals of Applied Statistics, 5(2A):969-93, doi:10.1214/10-AOAS397
Dobra, A., et al. (2011). Bayesian inference for general Gaussian graphical models with application to multivariate lattice data. Journal of the American Statistical Association, 106(496):1418-33, doi:10.1198/jasa.2011.tm10465
Mohammadi, A. and Dobra, A. (2017). The R Package BDgraph for Bayesian Structure Learning in Graphical Models, ISBA Bulletin, 24(4):11-16
Lenkoski, A. (2013). A direct sampler for G-Wishart variates, Stat, 2(1):119-28, doi:10.1002/sta4.23
Pensar, J. et al (2017) Marginal pseudo-likelihood learning of discrete Markov network structures, Bayesian Analysis, 12(4):1195-215, doi:10.1214/16-BA1032
See Also
bdgraph, bdgraph.mpl, bdgraph.dw, bdgraph.sim, compare, rgwish
Examples
## Not run:
library( BDgraph )
set.seed( 10 )
# Generating multivariate normal data from a 'scale-free' graph
data.sim <- bdgraph.sim( n = 100, p = 10, graph = "scale-free", vis = TRUE )
# Running algorithm based on GGMs
bdgraph.obj <- bdgraph( data = data.sim, iter = 5000 )
summary( bdgraph.obj )
# To compare the result with true graph
compare( bdgraph.obj, data.sim, main = c( "Target", "BDgraph" ), vis = TRUE )
# Confusion Matrix
conf.mat( actual = data.sim, pred = bdgraph.obj )
conf.mat.plot( actual = data.sim, pred = bdgraph.obj )
# Running algorithm based on GGMs and marginal pseudo-likelihood
bdgraph.mpl.obj <- bdgraph.mpl( data = data.sim, iter = 5000 )
summary( bdgraph.mpl.obj )
# Confusion Matrix
conf.mat( actual = data.sim, pred = bdgraph.mpl.obj )
conf.mat.plot( actual = data.sim, pred = bdgraph.mpl.obj )
# To compare the results of both algorithms with true graph
compare( list( bdgraph.obj, bdgraph.mpl.obj ), data.sim,
main = c( "Target", "BDgraph", "BDgraph_mpl" ), vis = TRUE )
## End(Not run)
The Discrete Weibull Distribution (Type 1)
Description
Density, distribution function, quantile function and random generation for the discrete Weibull distribution (type I) with parameters q and \beta.
Usage
ddweibull( x, q = exp( -1 ), beta = 1, zero = TRUE )
pdweibull( x, q = exp( -1 ), beta = 1, zero = TRUE )
qdweibull( p, q = exp( -1 ), beta = 1, zero = TRUE )
rdweibull( n, q = exp( -1 ), beta = 1, zero = TRUE )
Arguments
x |
vector of quantiles. |
p |
vector of probabilities. |
q, beta |
shape and scale parameters, the latter defaulting to 1. |
zero |
logical; if |
n |
number of observations. If |
Details
The discrete Weibull distribution has density given by
f(x) = q^{x^\beta} - q^{(x+1)^\beta}, x = 0, 1, 2, \ldots
For the case zero = FALSE:
f(x) = q^{(x-1)^\beta} - q^{x^\beta}, x = 1, 2, \ldots
Cumulative distribution function
F(x) = 1-q^{(x+1)^\beta}
For the case zero = FALSE, x+1 should replaced by x.
Value
ddweibull gives the density, pdweibull gives the distribution function, qdweibull gives the quantile function, and rdweibull generates random values.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl, Pariya Behrouzi, Veronica Vinciotti
References
Nakagawa, T. and Osaki, S. (1975). The Discrete Weibull Distribution. IEEE Transactions on Reliability, R-24, 300-301, doi:10.1109/TR.1975.5214915
See Also
Examples
n = 1000
q = 0.4
beta = 0.8
set.seed( 7 )
rdw = rdweibull( n = n, q = q, beta = beta )
plot( prop.table( table( rdw ) ), type = "h", col = "gray50" )
x = 0:max( rdw )
lines( x, ddweibull( x = x, q = q, beta = beta ), type = "o", col = "blue", lwd = 2 )
hist( pdweibull( x = rdw, q = q, beta = beta ) )
plot( ecdf( rdw ) )
lines( x, pdweibull( x, q = q, beta = beta ), col = "blue", lwd = 2, type = "s" )
Extract links from an adjacency matrix
Description
Extract links from an adjacency matrix or an object of calsses "sim" from function bdgraph.sim and
"graph" from function graph.sim.
Usage
adj2link( adj ) Arguments
adj |
adjacency matrix corresponding to a graph structure in which |
Value
matrix corresponding to the extracted links from graph structure.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
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, doi:10.18637/jss.v089.i03
See Also
Examples
# Generating a 'random' graph
adj <- graph.sim( p = 6, vis = TRUE )
adj2link( adj )
Compute the area under the ROC curve
Description
This function computes the numeric value of area under the ROC curve (AUC) specifically for graph structure learning.
Usage
auc( pred, actual, cut = 200, calibrate = TRUE )
Arguments
pred |
adjacency matrix corresponding to an estimated graph.
It can be an object with |
actual |
adjacency matrix corresponding to the actual graph structure in which |
cut |
number of cut points. |
calibrate |
If |
Value
The numeric AUC value
Author(s)
Reza Mohammadi a.mohammadi@uva.nl; Lucas Vogels l.f.o.vogels@uva.nl
References
Tom Fawcett (2006) “An introduction to ROC analysis”. Pattern Recognition Letters 27, 861–874, doi:10.1016/j.patrec.2005.10.010
Xavier Robin, Natacha Turck, Alexandre Hainard, et al. (2011) “pROC: an open-source package for R and S+ to analyze and compare ROC curves”. BMC Bioinformatics, 7, 77, doi:10.1186/1471-2105-12-77.
See Also
plotroc, pROC::plot.roc(), pROC::auc(), pROC::print.roc(), bdgraph, bdgraph.mpl, compare
Examples
## Not run:
set.seed( 5 )
# Generating multivariate normal data from a 'scale-free' graph
data.sim = bdgraph.sim( n = 200, p = 15, graph = "scale-free", vis = TRUE )
# Running BDMCMC algorithm
sample.bdmcmc = bdgraph( data = data.sim, algorithm = "bdmcmc", iter = 10000 )
BDgraph::auc( pred = sample.bdmcmc, actual = data.sim, calibrate = TRUE )
## End(Not run)
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 )
Arguments
data |
there are two options: (1) an ( |
n |
number of observations. It is needed if the " |
method |
character with two options " |
algorithm |
character with two options " |
iter |
number of iteration for the sampling algorithm. |
burnin |
number of burn-in iteration for the sampling algorithm. |
not.cont |
for the case |
g.prior |
for determining the prior distribution of each edge in the graph.
There are two options: a single value between |
df.prior |
degree of freedom for G-Wishart distribution, |
g.start |
corresponds to a starting point of the graph. It could be an ( |
jump |
it is only for 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 |
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 |
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. |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl 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, 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, 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, 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, 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, doi:10.1214/18-AOAS1164
Vogels, L., Mohammadi, R., Schoonhoven, M., and Birbil, S.I. (2023) Bayesian Structure Learning in Undirected Gaussian Graphical Models: Literature Review with Empirical Comparison, arXiv preprint, doi:10.48550/arXiv.2307.02603
Mohammadi, R., Schoonhoven, M., Vogels, L., and Birbil, S.I. (2023) Large-scale Bayesian Structure Learning for Gaussian Graphical Models using Marginal Pseudo-likelihood, arXiv preprint, 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
## Not run:
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 )
## End(Not run)
Search algorithm for Gaussian copula graphical models for count data
Description
This function consists of several sampling algorithms for Bayesian structure learning in undirected graphical models for count data. It is based on Gaussian copula graphical models with discrete Weibull distributed marginals.
To speed up the computations, the birth-death MCMC sampling algorithms are implemented in parallel using OpenMP in C++.
Usage
bdgraph.dw( data, x = NULL, formula = y ~ .,
n = NULL, algorithm = "bdmcmc", iter = 5000,
burnin = iter / 2, g.prior = 0.2, df.prior = 3,
ZI = FALSE, iter_bdw = 5000,
g.start = "empty", jump = NULL, save = FALSE,
q = NULL, beta = NULL, pii = NULL,
cores = NULL, threshold = 1e-8, verbose = TRUE )
Arguments
data |
( |
x |
( |
formula |
object of class formula as a symbolic description of the model for linking each node to the predictors. For the case of |
n |
number of observations. It is needed if the " |
algorithm |
character with two options " |
iter |
number of iterations for the sampling algorithm for graph learning. |
burnin |
number of burn-in iterations for the sampling algorithm for graph learning. |
g.prior |
for determining the prior distribution of each edge in the graph.
There are two options: a single value between |
df.prior |
degree of freedom for G-Wishart distribution, |
ZI |
logical. If FALSE (default), the conditional distribution of each response variable is assumed to be Discrete Weibull given the predictors |
iter_bdw |
number of iterations for the sampling algorithm to estimate the regression parameters for the Discrete Weibull distribution. It is passed to the |
g.start |
corresponds to a starting point of the graph. It could be an ( |
jump |
it is only for the BDMCMC algorithm ( |
save |
logical: if FALSE (default), the adjacency matrices are NOT saved. If TRUE, the adjacency matrices after burn-in are saved. |
q, beta |
parameters of the discrete Weibull distribution used for the marginals. They should be given either as a ( |
pii |
vector or matrix of zero-inflation parameters of the zero-inflated discrete Weibull distributions used for the marginals. If NULL (default), this parameter is estimated by the |
cores |
number of cores to use for parallel execution.
The case |
threshold |
threshold value for the convergence of the sampling algorithm from G-Wishart for the precision matrix. |
verbose |
logical: if TRUE (default), report/print the MCMC running time. |
Value
An object with S3 class "bdgraph" is returned, containing:
p_links |
upper triangular matrix corresponding to the estimated posterior probabilities of all possible links. |
K_hat |
posterior estimation of the precision matrix. |
sample_marginals |
posterior samples of the regression coefficients of the marginal distributions. |
For the case "save = TRUE", the code returns:
sample_graphs |
vector of strings which includes the adjacency matrices of the graphs visited after burn-in. |
graph_weights |
vector which includes the waiting times of the graphs visited 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 BDMCMC algorithm. |
all_weights |
vector which includes the waiting times for all iterations after burn-in. It is needed for monitoring the convergence of the BDMCMC algorithm. |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl, Veronica Vinciotti, and Pariya Behrouzi
References
Vinciotti, V., Behrouzi, P., and Mohammadi, R. (2022) Bayesian structural learning of microbiota systems from count metagenomic data, arXiv preprint, doi:10.48550/arXiv.2203.10118
Peluso, A., Vinciotti, V., and Yu, K. (2018) Discrete Weibull generalized additive model: an application to count fertility, Journal of the Royal Statistical Society: Series C, 68(3):565-583, doi:10.1111/rssc.12311
Haselimashhadi, H., Vinciotti, V., and Yu, K. (2018) A novel Bayesian regression model for counts with an application to health data, Journal of Applied Statistics, 45(6):1085-1105, doi:10.1080/02664763.2017.1342782
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, 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, doi:10.1214/14-BA889
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, doi:10.1111/rssc.12171
Mohammadi, R., Massam, H. and Letac, G. (2023). Accelerating Bayesian Structure Learning in Sparse Gaussian Graphical Models, Journal of the American Statistical Association, doi:10.1080/01621459.2021.1996377
See Also
bdgraph, bdgraph.mpl, bdw.reg, bdgraph.sim, summary.bdgraph, compare
Examples
## Not run:
# - - Example 1
# Generating multivariate Discrete Weibull data based on 'random' graph
data.sim <- bdgraph.sim( n = 100, p = 10, type = "dw", vis = TRUE )
bdgraph.obj <- bdgraph.dw( data = data.sim, iter = 5000 )
summary( bdgraph.obj )
# To compare the result with true graph
compare( bdgraph.obj, data.sim, main = c( "Target", "BDgraph" ), vis = TRUE )
# - - Example 2
# Generating multivariate Discrete Weibull data based on a 'scale-free' graph
data.sim <- bdgraph.sim( n = 100, p = 10, type = "dw", graph = "scale-free", vis = TRUE )
bdgraph.obj <- bdgraph.dw( data = data.sim, iter = 10000 )
summary( bdgraph.obj )
compare( bdgraph.obj, data.sim, main = c( "Target", "BDgraph" ), vis = TRUE )
## End(Not run)
Search algorithm in graphical models using marginal pseudo-likehlihood
Description
This function consists of several sampling algorithms for Bayesian model determination in undirected graphical models based on mariginal pseudo-likelihood.
To speed up the computations, the birth-death MCMC sampling algorithms are implemented in parallel using OpenMP in C++.
Usage
bdgraph.mpl( data, n = NULL, method = "ggm", transfer = TRUE,
algorithm = "bdmcmc", iter = 5000, burnin = iter / 2,
g.prior = 0.2, g.start = "empty",
jump = NULL, alpha = 0.5, save = FALSE,
cores = NULL, operator = "or", verbose = TRUE )
Arguments
data |
there are two options: (1) an ( |
n |
number of observations. It is needed if the " |
method |
character with two options " |
transfer |
for only |
algorithm |
character with two options " |
iter |
number of iteration for the sampling algorithm. |
burnin |
number of burn-in iteration for the sampling algorithm. |
g.prior |
for determining the prior distribution of each edge in the graph.
There are two options: a single value between |
g.start |
corresponds to a starting point of the graph. It could be an ( |
jump |
it is only for the BDMCMC algorithm ( |
alpha |
value of the hyper parameter of Dirichlet, which is a prior distribution. |
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 |
operator |
character with two options " |
verbose |
logical: if TRUE (default), report/print the MCMC running time. |
Value
An object with S3 class "bdgraph" is returned:
p_links |
upper triangular matrix which corresponds the estimated posterior probabilities of all possible links. |
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. |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl, Adrian Dobra, and Johan Pensar
References
Mohammadi, R., Schoonhoven, M., Vogels, L., and Birbil, S.I. (2023) Large-scale Bayesian Structure Learning for Gaussian Graphical Models using Marginal Pseudo-likelihood, arXiv preprint, doi:10.48550/arXiv.2307.00127
Dobra, A. and Mohammadi, R. (2018). Loglinear Model Selection and Human Mobility, Annals of Applied Statistics, 12(2):815-845, doi:10.1214/18-AOAS1164
Mohammadi, A. and Wit, E. C. (2015). Bayesian Structure Learning in Sparse Gaussian Graphical Models, Bayesian Analysis, 10(1):109-138, doi:10.1214/14-BA889
Vogels, L., Mohammadi, R., Schoonhoven, M., and Birbil, S.I. (2023) Bayesian Structure Learning in Undirected Gaussian Graphical Models: Literature Review with Empirical Comparison, arXiv preprint, doi:10.48550/arXiv.2307.02603
Mohammadi, A. and Dobra, A. (2017). The R Package BDgraph for Bayesian Structure Learning in Graphical Models, ISBA Bulletin, 24(4):11-16
Pensar, J. et al (2017) Marginal pseudo-likelihood learning of discrete Markov network structures, Bayesian Analysis, 12(4):1195-215, doi:10.1214/16-BA1032
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, doi:10.18637/jss.v089.i03
See Also
bdgraph, bdgraph.dw, bdgraph.sim, summary.bdgraph, compare
Examples
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 70, p = 5, size = 7, vis = TRUE )
bdgraph.obj <- bdgraph.mpl( data = data.sim, iter = 500 )
summary( bdgraph.obj )
# To compare the result with true graph
compare( bdgraph.obj, data.sim, main = c( "Target", "BDgraph" ) )
Nonparametric transfer
Description
Transfers non-Gaussian data to Gaussian.
Usage
bdgraph.npn( data, npn = "shrinkage", npn.thresh = NULL ) Arguments
data |
( |
npn |
character with three options |
npn.thresh |
truncation threshold; it is only for the truncated transformation ( |
Value
(n \times p) matrix of transferred data, if npn = "shrinkage" or "truncation", and
a non-paranormal correlation (p \times p) matrix, if npn = "skeptic".
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
References
Liu, H., et al (2012). High Dimensional Semiparametric Gaussian Copula Graphical Models, Annals of Statistics, 40(4):2293-2326
Zhao, T. and Liu, H. (2012). The huge Package for High-dimensional Undirected Graph Estimation in R, Journal of Machine Learning Research, 13:1059-1062
See Also
bdgraph.sim, bdgraph, bdgraph.mpl
Examples
## Not run:
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 6, p = 4, size = 4 )
data <- ( data.sim $ data - 3 ) ^ 4
data
# Transfer the data by truncation
bdgraph.npn( data, npn = "truncation" )
# Transfer the data by shrunken
bdgraph.npn( data, npn = "shrunken" )
# Transfer the data by skeptic
bdgraph.npn( data, npn = "skeptic" )
## End(Not run)
Graph data simulation
Description
Simulating multivariate distributions with different types of underlying graph structures, including
"random", "cluster", "smallworld", "scale-free", "lattice", "hub", "star", "circle", "AR(1)", and "AR(2)".
Based on the underlying graph structure, the function generates different types of multivariate data, including "Gaussian", "non-Gaussian", "categorical", "pois" (Poisson), "nbinom" (negative binomial), "dweibull" (discrete Weibull), "binary", "t" (t-distribution), "alternative-t", or "mixed" data.
This function can be used also for simulating only graphs by setting the option n=0 (default).
Usage
bdgraph.sim( p = 10, graph = "random", n = 0, type = "Gaussian", prob = 0.2,
size = NULL, mean = 0, class = NULL, cut = 4, b = 3,
D = diag( p ), K = NULL, sigma = NULL,
q = exp(-1), beta = 1, vis = FALSE, rewire = 0.05,
range.mu = c( 3, 5 ), range.dispersion = c( 0.01, 0.1 ), nu = 1 )
Arguments
p |
number of variables (nodes). |
graph |
graph structure with options
" |
n |
number of samples required. Note that for the case |
type |
type of data with options " |
prob |
if |
size |
number of links in the true graph (graph size). |
mean |
vector specifying the mean of the variables. |
class |
if |
cut |
if |
b |
degree of freedom for G-Wishart distribution, |
D |
positive definite |
K |
if |
sigma |
if |
q, beta |
if
They can be given either as a vector of length p or as an ( |
vis |
visualize the true graph structure. |
rewire |
rewiring probability for smallworld network. Must be between 0 and 1. |
range.mu, range.dispersion |
if |
nu |
if |
Value
An object with S3 class "sim" is returned:
data |
generated data as an ( |
sigma |
covariance matrix of the generated data. |
K |
precision matrix of the generated data. |
G |
adjacency matrix corresponding to the true graph structure. |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl, Pariya Behrouzi, Veronica Vinciotti, Ernst Wit, and Alexander Christensen
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, doi:10.18637/jss.v089.i03
See Also
graph.sim, bdgraph, bdgraph.mpl
Examples
## Not run:
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( p = 10, n = 50, prob = 0.3, vis = TRUE )
print( data.sim )
# Generating multivariate normal data from a 'hub' graph
data.sim <- bdgraph.sim( p = 6, n = 3, graph = "hub", vis = FALSE )
round( data.sim $ data, 2 )
# Generating mixed data from a 'hub' graph
data.sim <- bdgraph.sim( p = 8, n = 10, graph = "hub", type = "mixed" )
round( data.sim $ data, 2 )
# Generating only a 'scale-free' graph (with no data)
graph.sim <- bdgraph.sim( p = 8, graph = "scale-free" )
plot( graph.sim )
graph.sim $ G
## End(Not run)
Bayesian estimation of (zero-inflated) Discrete Weibull regression
Description
Bayesian estimation of the parameters for Discrete Weibull (DW) regression. The conditional distribution of the response given the predictors is assumed to be DW with parameters q and beta, dependent on the predictors, and, with an additional parameter pi under zero inflation.
Usage
bdw.reg( data, formula = NA, iter = 5000, burnin = NULL,
dist.q = dnorm, dist.beta = dnorm,
par.q = c( 0, 1 ), par.beta = c( 0, 1 ), par.pi = c( 1, 1 ),
initial.q = NULL, initial.beta = NULL, initial.pi = NULL,
ZI = FALSE, scale.proposal = NULL, adapt = TRUE, print = TRUE )
Arguments
data |
|
formula |
object of class formula as a symbolic description of the model to be fitted. For the case of |
iter |
number of iterations for the sampling algorithm. |
burnin |
number of burn-in iterations for the sampling algorithm. |
dist.q |
Prior density for the regression coefficients associated to the parameter |
dist.beta |
Prior density for the regression coefficients associated to the parameter |
par.q |
vector of length two corresponding to the parameters of |
par.beta |
vector of length two corresponding to the parameters of |
par.pi |
vector of length two corresponding to the parameters of the |
initial.q, initial.beta, initial.pi |
vector of initial values for the regression coefficients and for |
ZI |
logical: if FALSE (default), the conditional distribution of the response given the predictors is assumed to be DW with parameters |
scale.proposal |
scale of the proposal function. Setting to lower values results in an increase in the acceptance rate of the sampler. |
adapt |
logical: if TRUE (default), the proposals will be adapted. If FALSE, no adapting will be applied. |
print |
logical: if TRUE (default), tracing information is printed. |
Details
The regression model uses a logit link function on q and a log link function on beta, the two parameters of a DW distribution, with probability mass function given by
DW(y) = q^{y^\beta} - q^{(y+1)^\beta}, y = 0, 1, 2, \ldots
For the case of zero inflation (ZI = TRUE), a zero-inflated DW is considered:
f(y) = (1 - pi) I(y = 0) + pi DW(y)
where 0 \leq pi \leq 1 and I(y = 0) is an indicator for the point mass at zero for the response y.
Value
sample |
MCMC samples |
q.est |
posterior estimates of |
beta.est |
posterior estimates of |
pi.est |
posterior estimates of |
accept.rate |
acceptance rate of the MCMC algorithm |
Author(s)
Veronica Vinciotti, Reza Mohammadi a.mohammadi@uva.nl, and Pariya Behrouzi
References
Vinciotti, V., Behrouzi, P., and Mohammadi, R. (2022) Bayesian structural learning of microbiota systems from count metagenomic data, arXiv preprint, doi:10.48550/arXiv.2203.10118
Peluso, A., Vinciotti, V., and Yu, K. (2018) Discrete Weibull generalized additive model: an application to count fertility, Journal of the Royal Statistical Society: Series C, 68(3):565-583, doi:10.1111/rssc.12311
Haselimashhadi, H., Vinciotti, V. and Yu, K. (2018) A novel Bayesian regression model for counts with an application to health data, Journal of Applied Statistics, 45(6):1085-1105, doi:10.1080/02664763.2017.1342782
See Also
bdgraph.dw, bdgraph, ddweibull, bdgraph.sim
Examples
## Not run:
# - - Example 1
q = 0.6
beta = 1.1
n = 500
y = BDgraph::rdweibull( n = n, q = q, beta = beta )
output = bdw.reg( data = y, y ~ ., iter = 5000 )
output $ q.est
output $ beta.est
traceplot( output $ sample[ , 1 ], acf = T, pacf = T )
traceplot( output $ sample[ , 2 ], acf = T, pacf = T )
# - - Example 2
q = 0.6
beta = 1.1
pii = 0.8
n = 500
y_dw = BDgraph::rdweibull( n = n, q = q, beta = beta )
z = rbinom( n = n, size = 1, prob = pii )
y = z * y_dw
output = bdw.reg( data = y, iter = 5000, ZI = TRUE )
output $ q.est
output $ beta.est
output $ pi.est
traceplot( output $ sample[ , 1 ], acf = T, pacf = T )
traceplot( output $ sample[ , 2 ], acf = T, pacf = T )
traceplot( output $ sample[ , 3 ], acf = T, pacf = T )
# - - Example 3
theta.q = c( 0.1, -0.1, 0.34 ) # true parameter
theta.beta = c( 0.1, -.15, 0.5 ) # true parameter
n = 500
x1 = runif( n = n, min = 0, max = 1.5 )
x2 = runif( n = n, min = 0, max = 1.5 )
reg_q = theta.q[ 1 ] + x1 * theta.q[ 2 ] + x2 * theta.q[ 3 ]
q = 1 / ( 1 + exp( - reg_q ) )
reg_beta = theta.beta[ 1 ] + x1 * theta.beta[ 2 ] + x2 * theta.beta[ 3 ]
beta = exp( reg_beta )
y = BDgraph::rdweibull( n = n, q = q, beta = beta )
data = data.frame( x1, x2, y )
output = bdw.reg( data, y ~. , iter = 5000 )
# - - Example 4
theta.q = c( 1, -1, 0.8 ) # true parameter
theta.beta = c( 1, -1, 0.3 ) # true parameter
pii = 0.8
n = 500
x1 = runif( n = n, min = 0, max = 1.5 )
x2 = runif( n = n, min = 0, max = 1.5 )
reg_q = theta.q[ 1 ] + x1 * theta.q[ 2 ] + x2 * theta.q[ 3 ]
q = 1 / ( 1 + exp( - reg_q ) )
reg_beta = theta.beta[ 1 ] + x1 * theta.beta[ 2 ] + x2 * theta.beta[ 3 ]
beta = exp( reg_beta )
y_dw = BDgraph::rdweibull( n = n, q = q, beta = beta )
z = rbinom( n = n, size = 1, prob = pii )
y = z * y_dw
data = data.frame( x1, x2, y )
output = bdw.reg( data, y ~. , iter = 5000, ZI = TRUE )
## End(Not run)
Bayes factor for two graphs
Description
Compute the Bayes factor for two graph structures.
Usage
bf( num, den, bdgraph.obj, log = TRUE )
Arguments
num, den |
adjacency matrix corresponding to the true graph structure in which |
bdgraph.obj |
object of |
log |
character value. If TRUE the Bayes factor is given as log(BF). |
Value
single numeric value, the Bayes factor of the two graph structures num and den.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
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, doi:10.18637/jss.v089.i03
See Also
bdgraph, bdgraph.mpl, compare, bdgraph.sim
Examples
## Not run:
# Generating multivariate normal data from a 'circle' graph
data.sim <- bdgraph.sim( n = 50, p = 6, graph = "circle", vis = TRUE )
# Running sampling algorithm
bdgraph.obj <- bdgraph( data = data.sim )
graph_1 <- graph.sim( p = 6, vis = TRUE )
graph_2 <- graph.sim( p = 6, vis = TRUE )
bf( num = graph_1, den = graph_2, bdgraph.obj = bdgraph.obj )
## End(Not run)
Graph structure comparison
Description
This function provides several measures to assess the performance of the graphical structure learning.
Usage
compare( pred, actual, main = NULL, vis = FALSE ) Arguments
pred |
adjacency matrix corresponding to an estimated graph.
It can be an object with |
actual |
adjacency matrix corresponding to the true graph structure in which |
main |
character vector giving the names for the result table. |
vis |
logical: if TRUE, visualize the true graph and estimated graph structures. |
Value
True positive |
number of correctly estimated links. |
True negative |
number of true non-existing links which is correctly estimated. |
False positive |
number of links which they are not in the true graph, but are incorrectly estimated. |
False negative |
number of links which they are in the true graph, but are not estimated. |
F1-score |
weighted average of the |
Specificity |
Specificity value reaches its best value at 1 and worst score at 0. |
Sensitivity |
Sensitivity value reaches its best value at 1 and worst score at 0. |
MCC |
Matthews Correlation Coefficients (MCC) value reaches its best value at 1 and worst score at 0. |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl, Antonio Abbruzzo, and Ivan Vujacic
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, doi:10.18637/jss.v089.i03
See Also
bdgraph, bdgraph.mpl, bdgraph.sim, plotroc
Examples
## Not run:
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 50, p = 6, size = 7, vis = TRUE )
# Running sampling algorithm based on GGMs
sample.ggm <- bdgraph( data = data.sim, method = "ggm", iter = 10000 )
# Comparing the results
compare( sample.ggm, data.sim, main = c( "True", "GGM" ), vis = TRUE )
# Running sampling algorithm based on GCGMs
sample.gcgm <- bdgraph( data = data.sim, method = "gcgm", iter = 10000 )
# Comparing GGM and GCGM methods
compare( list( sample.ggm, sample.gcgm ), data.sim,
main = c( "True", "GGM", "GCGM" ), vis = TRUE )
## End(Not run)
Confusion Matrix
Description
Create a Confusion Matrix.
Usage
conf.mat( pred, actual, cutoff = 0.5, proportion = FALSE,
dnn = c( "Prediction", "Actual" ), ... )
Arguments
pred |
adjacency matrix corresponding to an estimated graph.
It can be an object with |
actual |
adjacency matrix corresponding to the actual graph structure in which |
cutoff |
cutoff value for the case that |
proportion |
logical: FALSE (default) for a confusion matrix with number of cases. TRUE, for a confusion matrix with the proportion of cases. |
dnn |
names to be given to the dimensions in the result (the dimnames names). |
... |
further arguments to be passed to |
Value
the results of table on pred and actual.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
See Also
conf.mat.plot, compare, roc, bdgraph
Examples
## Not run:
set.seed( 100 )
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 50, p = 6, size = 7, vis = TRUE )
# Running sampling algorithm based on GGMs
sample.ggm <- bdgraph( data = data.sim, method = "ggm", iter = 10000 )
# Confusion Matrix for GGM method
conf.mat( pred = sample.ggm, actual = data.sim )
## End(Not run)
Plot Confusion Matrix
Description
Plot a Confusion Matrix.
Usage
conf.mat.plot( pred, actual, cutoff = 0.5, conf.level = 0, margin = 1,
color = c( "#ff83a8", "#83ff9b" ), ... )
Arguments
pred |
adjacency matrix corresponding to an estimated graph.
It can be an object with |
actual |
adjacency matrix corresponding to the actual graph structure in which |
cutoff |
cutoff value for the case that |
conf.level |
confidence level used for the confidence rings on the odds ratios. Must be a single nonnegative number less than 1; if set to 0 (the default), confidence rings are suppressed. |
margin |
numeric vector with the margins to equate. Must be one of 1 (the default), 2, or c(1, 2), which corresponds to standardizing the row, column, or both margins in each 2 by 2 table. Only used if std equals "margins". |
color |
vector of length 2 specifying the colors to use for the smaller and larger diagonals of each 2 by 2 table. |
... |
options to be passed to |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
See Also
conf.mat, compare, roc, bdgraph
Examples
## Not run:
set.seed( 100 )
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 50, p = 6, size = 7, vis = TRUE )
# Running sampling algorithm based on GGMs
sample.ggm <- bdgraph( data = data.sim, method = "ggm", iter = 10000 )
# Confusion Matrix for GGM method
conf.mat.plot( pred = sample.ggm, actual = data.sim )
## End(Not run)
Estimated covariance matrix
Description
Provides the estimated covariance matrix.
Usage
covariance( bdgraph.obj, round = 2 ) Arguments
bdgraph.obj |
object of |
round |
value for rounding all probabilities to the specified number of decimal places. |
Value
matrix which corresponds the estimated covariance matrix.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
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, 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, 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, doi:10.1080/01621459.2021.1996377
See Also
Examples
## Not run:
# Generating multivariate normal data from a 'circle' graph
data.sim <- bdgraph.sim( n = 70, p = 6, graph = "circle", vis = TRUE )
bdgraph.obj <- bdgraph( data = data.sim )
covariance( bdgraph.obj ) # Estimated covariance matrix
data.sim $ sigma # True covariance matrix
## End(Not run)
Human gene expression dataset
Description
The dataset contains human gene expression of 100 transcripts (with unique Illumina TargetID) measured on 60 unrelated individuals.
Usage
data( geneExpression ) Format
The format is a matrix with 60 rows (number of individuals) and 100 column (number of transcripts).
References
Bhadra, A. and Mallick, B. K. (2013). Joint High Dimensional Bayesian Variable and Covariance Selection with an Application to eQTL Analysis, Biometrics, 69(2):447-457, doi:10.1111/biom.12021
Mohammadi, A. and Wit, E. C. (2015). Bayesian Structure Learning in Sparse Gaussian Graphical Models, Bayesian Analysis, 10(1):109-138, doi:10.1214/14-BA889
Examples
data( geneExpression )
dim( geneExpression )
head( geneExpression )
Normalizing constant for G-Wishart
Description
Calculates log of the normalizing constant of G-Wishart distribution based on the Monte Carlo method, developed by Atay-Kayis and Massam (2005).
Usage
gnorm( adj, b = 3, D = diag( ncol( adj ) ), iter = 100 )
Arguments
adj |
adjacency matrix corresponding to the graph structure. It is an upper triangular matrix in which
|
b |
degree of freedom for G-Wishart distribution, |
D |
positive definite |
iter |
number of iteration for the Monte Carlo approximation. |
Details
Log of the normalizing constant approximation using Monte Carlo method for a G-Wishart distribution, K \sim W_G(b, D), with density:
Pr(K) = \frac{1}{I(b, D)} |K| ^ {(b - 2) / 2} \exp \left\{- \frac{1}{2} \mbox{trace}(K \times D)\right\}.
Value
Log of the normalizing constant of G-Wishart distribution.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
References
Atay-Kayis, A. and Massam, H. (2005). A monte carlo method for computing the marginal likelihood in nondecomposable Gaussian graphical models, Biometrika, 92(2):317-335, doi:10.1093/biomet/92.2.317
Mohammadi, R., Massam, H. and Letac, G. (2023). Accelerating Bayesian Structure Learning in Sparse Gaussian Graphical Models, Journal of the American Statistical Association, doi:10.1080/01621459.2021.1996377
Uhler, C., et al (2018) Exact formulas for the normalizing constants of Wishart distributions for graphical models, The Annals of Statistics 46(1):90-118, doi:10.1214/17-AOS1543
See Also
Examples
## Not run:
# adj: adjacency matrix of graph with 3 nodes and 2 links
adj <- matrix( c( 0, 0, 1,
0, 0, 1,
0, 0, 0 ), 3, 3, byrow = TRUE )
gnorm( adj, b = 3, D = diag( 3 ) )
## End(Not run)
Graph simulation
Description
Simulating undirected graph structures, including
"random", "cluster", "scale-free", "lattice", "hub", "star", and "circle".
Usage
graph.sim( p = 10, graph = "random", prob = 0.2, size = NULL, class = NULL, vis = FALSE,
rewire = 0.05 )
Arguments
p |
number of variables (nodes). |
graph |
undirected graph with options
" |
prob |
if |
size |
number of links in the true graph (graph size). |
class |
if |
vis |
visualize the true graph structure. |
rewire |
rewiring probability for smallworld network. Must be between 0 and 1. |
Value
The adjacency matrix corresponding to the simulated graph structure, as an object with S3 class "graph".
Author(s)
Reza Mohammadi a.mohammadi@uva.nl and Alexander Christensen
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, doi:10.18637/jss.v089.i03
See Also
bdgraph.sim, bdgraph, bdgraph.mpl
Examples
# Generating a 'hub' graph
adj <- graph.sim( p = 8, graph = "scale-free" )
plot( adj )
adj
Extract links from an adjacency matrix
Description
Extract links from an adjacency matrix or an object of calsses "sim" from function bdgraph.sim and
"graph" from function graph.sim.
Usage
link2adj( link, p = NULL ) Arguments
link |
( |
p |
number of nodes of the graph. |
Value
An adjacency matrix corresponding to a graph structure in which a_{ij}=1 if there is a link between notes i and j, otherwise a_{ij}=0.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
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, doi:10.18637/jss.v089.i03
See Also
Examples
# Generating a 'random' graph
adj <- graph.sim( p = 6, vis = TRUE )
link <- adj2link( adj )
link2adj( link, p = 6 )
Graph structure comparison
Description
Computes (weighted) mean squared error.
Usage
mse( pred, actual, weight = FALSE ) Arguments
pred |
adjacency matrix corresponding to an estimated graph.
It can be an object with |
actual |
adjacency matrix corresponding to the true graph structure in which |
weight |
for the case of weighted MSE. |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl; Lucas Vogels l.f.o.vogels@uva.nl
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, doi:10.18637/jss.v089.i03
See Also
compare, auc, bdgraph, bdgraph.mpl, bdgraph.sim, plotroc
Examples
## Not run:
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 50, p = 6, size = 7, vis = TRUE )
# Running sampling algorithm based on GGMs
sample.ggm <- bdgraph( data = data.sim, method = "ggm", iter = 10000 )
# To compute the value of MSE
mse( pred = sample.ggm, actual = data.sim )
# To compute the value of weighted MSE
mse( pred = sample.ggm, actual = data.sim, weight = 0.5 )
## End(Not run)
Posterior probabilities of the graphs
Description
Provides the estimated posterior probabilities for the most likely graphs or a specific graph.
Usage
pgraph( bdgraph.obj, number.g = 4, adj = NULL ) Arguments
bdgraph.obj |
object of |
number.g |
number of graphs with the highest posterior probabilities to be shown.
This option is ignored if |
adj |
adjacency matrix corresponding to a graph structure. It is an upper triangular matrix in which
|
Value
selected_g |
adjacency matrices which corresponding to the graphs with the highest posterior probabilities. |
prob_g |
vector of the posterior probabilities of the graphs corresponding to |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl 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, 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, 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, doi:10.1080/01621459.2021.1996377
See Also
Examples
## Not run:
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 50, p = 6, size = 6, vis = TRUE )
bdgraph.obj <- bdgraph( data = data.sim, save = TRUE )
# Estimated posterior probability of the true graph
pgraph( bdgraph.obj, adj = data.sim )
# Estimated posterior probability of first and second graphs with highest probabilities
pgraph( bdgraph.obj, number.g = 2 )
## End(Not run)
Estimated posterior link probabilities
Description
Provides the estimated posterior link probabilities for all possible links in the graph.
Usage
plinks( bdgraph.obj, round = 2, burnin = NULL ) Arguments
bdgraph.obj |
object of |
round |
value for rounding all probabilities to the specified number of decimal places. |
burnin |
number of burn-in iteration to scape. |
Value
An upper triangular matrix which corresponds the estimated posterior probabilities for all possible links.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl 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, 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, 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, doi:10.1080/01621459.2021.1996377
Dobra, A. and Mohammadi, R. (2018). Loglinear Model Selection and Human Mobility, Annals of Applied Statistics, 12(2):815-845, doi:10.1214/18-AOAS1164
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, doi:10.1111/rssc.12171
See Also
Examples
## Not run:
# Generating multivariate normal data from a 'circle' graph
data.sim <- bdgraph.sim( n = 70, p = 6, graph = "circle", vis = TRUE )
bdgraph.obj <- bdgraph( data = data.sim, iter = 10000 )
plinks( bdgraph.obj, round = 2 )
## End(Not run)
Plot function for S3 class "bdgraph"
Description
Visualizes structure of the selected graphs which could be a graph with links for which their estimated posterior probabilities are greater than 0.5 or graph with the highest posterior probability.
Usage
## S3 method for class 'bdgraph'
plot( x, cut = 0.5, number.g = NULL, main = NULL,
layout = igraph::layout_with_fr, vertex.size = 2, vertex.color = "orange",
vertex.frame.color = "orange", vertex.label = NULL, vertex.label.dist = 0.5,
vertex.label.color = "blue", edge.color = "lightblue", ... ) Arguments
x |
object of |
cut |
threshold for including the links in the selected graph based on the estimated posterior probabilities of the links; See the examples. |
number.g |
number of graphs with the highest probabilities. This option works for the case running function |
main |
Graphical parameter (see plot). |
layout |
vertex placement which is according to |
vertex.size |
vertex size which is according to |
vertex.color |
vertex color which is according to |
vertex.frame.color |
vertex frame color which is according to |
vertex.label |
vertex label. The default vertex labels are the vertex ids. |
vertex.label.dist |
vertex label distance which is according to |
vertex.label.color |
vertex label color which is according to |
edge.color |
edge color which is according to |
... |
additional plotting parameters. For the complete list, see |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl 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, doi:10.18637/jss.v089.i03
See Also
Examples
## Not run:
set.seed( 100 )
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 100, p = 15, graph = "random", prob = 0.2, vis = TRUE )
bdgraph.obj <- bdgraph( data = data.sim )
plot( bdgraph.obj )
bdgraph.obj <- bdgraph( data = data.sim, save = TRUE )
plot( bdgraph.obj, cut = 0.5 )
plot( bdgraph.obj, number.g = 4 )
## End(Not run)
Plot function for S3 class "graph"
Description
Visualizes structure of the graph.
Usage
## S3 method for class 'graph'
plot( x, cut = 0.5, mode = "undirected", diag = FALSE, main = NULL,
layout = igraph::layout_with_fr, vertex.size = 2, vertex.color = "orange",
vertex.frame.color = "orange", vertex.label = NULL, vertex.label.dist = 0.5,
vertex.label.color = "blue", edge.color = "lightblue", ... )
Arguments
x |
object of |
cut |
for the case where input ' |
mode |
type of graph which is according to |
diag |
logical which is according to |
main |
graphical parameter (see plot). |
layout |
vertex placement which is according to |
vertex.size |
vertex size which is according to |
vertex.color |
vertex color which is according to |
vertex.frame.color |
vertex frame color which is according to |
vertex.label |
vertex label. The default vertex labels are the vertex ids. |
vertex.label.dist |
vertex label distance which is according to |
vertex.label.color |
vertex label color which is according to |
edge.color |
edge color which is according to |
... |
additional plotting parameters. For the complete list, see |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
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, doi:10.18637/jss.v089.i03
See Also
graph.sim, bdgraph.sim, plot.igraph
Examples
# Generating a 'scale-free' graph
adj <- graph.sim( p = 20, graph = "scale-free" )
plot( adj )
Plot function for S3 class "sim"
Description
Visualizes structure of the simulated graph for an object of S3 class "sim", from function bdgraph.sim.
Usage
## S3 method for class 'sim'
plot( x, ... )
Arguments
x |
object of |
... |
additional plotting parameters. See |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl 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, doi:10.18637/jss.v089.i03
See Also
graph.sim, bdgraph.sim, plot.graph, plot.igraph
Examples
set.seed( 10 )
# Generating synthetic multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 10, p = 15 )
plot( data.sim )
Convergence plot
Description
Visualizes the cumulative occupancy fractions of all possible links in the graph. It can be used for monitoring the convergence of the sampling algorithms, BDMCMC and RJMCMC.
Usage
plotcoda( bdgraph.obj, thin = NULL, control = TRUE, main = NULL,
verbose = TRUE, ... )
Arguments
bdgraph.obj |
object of |
thin |
option for getting fast result for a cumulative plot according to part of the iteration. |
control |
logical: if TRUE (default) and the number of nodes is greater than 15, then 100 links randomly is selected for visualization. |
main |
graphical parameter (see plot). |
verbose |
logical: if TRUE (default), report/print the calculation progress. |
... |
system reserved (no specific usage). |
Details
Note that a spending time for this function depends on the number of nodes.
For fast result, you can choose bigger value for the 'thin' option.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
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, doi:10.18637/jss.v089.i03
See Also
bdgraph, bdgraph.mpl, traceplot
Examples
## Not run:
# Generating multivariate normal data from a 'circle' graph
data.sim <- bdgraph.sim( n = 50, p = 6, graph = "circle", vis = TRUE )
bdgraph.obj <- bdgraph( data = data.sim, iter = 10000, burnin = 0 , save = TRUE )
plotcoda( bdgraph.obj )
## End(Not run)
ROC plot
Description
Draws the receiver operating characteristic (ROC) curve according to the true graph structure for object of S3 class "bdgraph", from function bdgraph.
Usage
plotroc( pred, actual, cut = 200, smooth = FALSE, calibrate = TRUE,
linetype = NULL, color = NULL, size = 1, main = "ROC Curve",
xlab = "False Postive Rate", ylab = "True Postive Rate",
legend = TRUE, legend.size = 17, legend.position = c( 0.7, 0.3 ),
labels = NULL, auc = TRUE, theme = ggplot2::theme_minimal() )
Arguments
pred |
upper triangular matrix corresponding to the estimated posterior probabilities for all possible links.
It can be an object with |
actual |
adjacency matrix corresponding to the true graph structure in which |
cut |
number of cut points. |
smooth |
logical: for smoothing the ROC curve. |
calibrate |
If |
linetype |
specification for the default plotting line type. |
color |
specification for the default plotting color. |
size |
specification for the default plotting line size. |
main |
overall title for the plot. |
xlab |
title for the x axis. |
ylab |
title for the y axis. |
legend |
logical: for adding legend to the ROC plot. |
legend.size |
title for the x axis. |
legend.position |
title for the y axis. |
labels |
for legends of the legend to the ROC plot. |
auc |
logical: to report AUC with legend. |
theme |
theme for the plot from the function |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl; Lucas Vogels l.f.o.vogels@uva.nl
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, 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, 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, doi:10.1080/01621459.2021.1996377
See Also
roc, pROC::plot.roc(), pROC::auc(), bdgraph, bdgraph.mpl, compare
Examples
## Not run:
# To generate multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 30, p = 6, size = 7, vis = TRUE )
# To Run sampling algorithm
bdgraph.obj <- bdgraph( data = data.sim, iter = 10000 )
# To compare the results
plotroc( bdgraph.ob2j, data.sim )
# To compare the results based on CGGMs approach
bdgraph.obj2 <- bdgraph( data = data.sim, method = "gcgm", iter = 10000 )
# To Compare the resultss
plotroc( list( bdgraph.obj, bdgraph.obj2 ), data.sim, legend = FALSE )
## End(Not run)
Posterior Predictive Samples
Description
Provides samples from the posterior predictive distribution.
Usage
posterior.predict( object, iter = 1, ... )
Arguments
object |
object of |
iter |
number of predictions. |
... |
additional parameters. |
Value
a matrix containing the predicted datasets, corresponding to the samples from the joint posterior disribtuion.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl 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, 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, 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, doi:10.1080/01621459.2021.1996377
Dobra, A. and Mohammadi, R. (2018). Loglinear Model Selection and Human Mobility, Annals of Applied Statistics, 12(2):815-845, doi:10.1214/18-AOAS1164
Vogels, L., Mohammadi, R., Schoonhoven, M., and Birbil, S.I. (2023) Bayesian Structure Learning in Undirected Gaussian Graphical Models: Literature Review with Empirical Comparison, arXiv preprint, doi:10.48550/arXiv.2307.02603
Mohammadi, R., Schoonhoven, M., Vogels, L., and Birbil, S.I. (2023) Large-scale Bayesian Structure Learning for Gaussian Graphical Models using Marginal Pseudo-likelihood, arXiv preprint, doi:10.48550/arXiv.2307.00127
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, doi:10.1111/rssc.12171
See Also
bdgraph, bdgraph.mpl, bdgraph.dw
Examples
## Not run:
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 50, p = 6, size = 7, vis = TRUE )
bdgraph.obj <- bdgraph( data = data.sim )
posterior.predict( bdgraph.obj, iter = 20 )
## End(Not run)
Estimated precision matrix
Description
Provides the estimated precision matrix.
Usage
precision( bdgraph.obj, round = 2 ) Arguments
bdgraph.obj |
object of |
round |
value for rounding all probabilities to the specified number of decimal places. |
Value
matrix which corresponds the estimated precision matrix.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
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, doi:10.18637/jss.v089.i03
See Also
Examples
## Not run:
# Generating multivariate normal data from a 'circle' graph
data.sim <- bdgraph.sim( n = 70, p = 6, graph = "circle", vis = TRUE )
bdgraph.obj <- bdgraph( data = data.sim )
precision( bdgraph.obj ) # Estimated precision matrix
data.sim $ K # True precision matrix
## End(Not run)
Predict function for S3 class "bdgraph"
Description
Provides predict values of the results for function bdgraph.
Usage
## S3 method for class 'bdgraph'
predict( object, iter = 1, ... )
Arguments
object |
object of |
iter |
number of predictions. |
... |
additional parameters. |
Value
a matrix containing the predicted datasets, corresponding to the samples from the joint posterior disribtuion.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl 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, 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, 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, doi:10.1080/01621459.2021.1996377
Dobra, A. and Mohammadi, R. (2018). Loglinear Model Selection and Human Mobility, Annals of Applied Statistics, 12(2):815-845, doi:10.1214/18-AOAS1164
Vogels, L., Mohammadi, R., Schoonhoven, M., and Birbil, S.I. (2023) Bayesian Structure Learning in Undirected Gaussian Graphical Models: Literature Review with Empirical Comparison, arXiv preprint, doi:10.48550/arXiv.2307.02603
Mohammadi, R., Schoonhoven, M., Vogels, L., and Birbil, S.I. (2023) Large-scale Bayesian Structure Learning for Gaussian Graphical Models using Marginal Pseudo-likelihood, arXiv preprint, doi:10.48550/arXiv.2307.00127
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, doi:10.1111/rssc.12171
See Also
bdgraph, bdgraph.mpl, bdgraph.dw
Examples
## Not run:
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 50, p = 6, size = 7, vis = TRUE )
bdgraph.obj <- bdgraph( data = data.sim )
predict( bdgraph.obj, iter = 20 )
## End(Not run)
Print function for S3 class "bdgraph"
Description
Prints the information about the selected graph which could be a graph with links for which their estimated posterior probabilities are greater than 0.5 or graph with the highest posterior probability. It provides adjacency matrix, size and posterior probability of the selected graph.
Usage
## S3 method for class 'bdgraph'
print( x, ... )Arguments
x |
object of |
... |
system reserved (no specific usage). |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl 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, doi:10.18637/jss.v089.i03
See Also
Examples
## Not run:
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 50, p = 6, vis = TRUE )
bdgraph.obj <- bdgraph( data = data.sim )
print( bdgraph.obj )
## End(Not run)
Print function for S3 class "sim"
Description
Prints the information about the type of data, the sample size, the graph type, the number of nodes, number of links and sparsity of the true graph.
Usage
## S3 method for class 'sim'
print( x, ... ) Arguments
x |
object of |
... |
system reserved (no specific usage). |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl 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, doi:10.18637/jss.v089.i03
See Also
Examples
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 20, p = 10, vis = TRUE )
print( data.sim )
Risk factors of coronary heart disease
Description
The dataset consist of 6 discrete variables as the potential risk factors of coronary heart disease.
The data collected from 1841 men employed of a car factory in Czechoslovakia (Reinis et al. 1981).
Usage
data( reinis ) Format
The format is a matrix with 1841 rows (number of individuals) and 6 column (number of variables).
References
Edwards and Havranek (1985). A fast procedure for model search in multidimensional contingency tables, Biometrika, 72:339-351
Reinis et al (1981). Prognostic significance of the risk profile in the prevention of coronary heart disease, Bratis. lek. Listy, 76:137-150
Mohammadi, A. and Dobra, A. (2017). The R Package BDgraph for Bayesian Structure Learning in Graphical Models, ISBA Bulletin, 24(4):11-16
Examples
data( reinis )
summary( reinis )
Sampling from G-Wishart distribution
Description
Generates random matrices, distributed according to the G-Wishart distribution with parameters b and D, W_G(b, D) with respect to the graph structure G.
Note this fuction works for both non-decomposable and decomposable graphs.
Usage
rgwish( n = 1, adj = NULL, b = 3, D = NULL, threshold = 1e-8 ) Arguments
n |
number of samples required. |
adj |
adjacency matrix corresponding to the graph structure which can be non-decomposable or decomposable. It should be an upper triangular matrix in which |
b |
degree of freedom for G-Wishart distribution, |
D |
positive definite |
threshold |
threshold value for the convergence of sampling algorithm from G-Wishart. |
Details
Sampling from G-Wishart distribution, K \sim W_G(b, D), with density:
Pr(K) \propto |K| ^ {(b - 2) / 2} \exp \left\{- \frac{1}{2} \mbox{trace}(K \times D)\right\},
which b > 2 is the degree of freedom and D is a symmetric positive definite matrix.
Value
A numeric array, say A, of dimension (p \times p \times n), where each A[,,i] is a positive
definite matrix, a realization of the G-Wishart distribution, W_G(b, D).
Note, for the case n=1, the output is a matrix.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
References
Lenkoski, A. (2013). A direct sampler for G-Wishart variates, Stat, 2:119-128, doi:10.1002/sta4.23
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, 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, doi:10.1214/14-BA889
See Also
Examples
# Generating a 'circle' graph as a non-decomposable graph
adj <- graph.sim( p = 5, graph = "circle" )
adj # adjacency of graph with 5 nodes
sample <- rgwish( n = 1, adj = adj, b = 3, D = diag( 5 ) )
round( sample, 2 )
sample <- rgwish( n = 5, adj = adj )
round( sample, 2 )
Generate data from the multivariate Normal distribution
Description
Random generation function from the multivariate Normal distribution with mean equal to mean and covariance matrix sigma.
Usage
rmvnorm( n = 10, mean = rep( 0, length = ncol( sigma ) ),
sigma = diag( length( mean ) ) )
Arguments
n |
Number of observations. |
mean |
Mean vector, default is |
sigma |
positive definite covariance matrix, default is |
Value
A numeric matrix with rows equal to n and columns equal to length( mean ).
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
See Also
Examples
mean <- c( 5, 20 )
sigma <- matrix( c( 4, 2,
2, 5 ), 2, 2 ) # covariance matrix
sample <- rmvnorm( n = 500, mean = mean, sigma = sigma )
plot( sample )
Build a ROC curve
Description
This function builds a ROC curve specifically for graph structure learning and returns a “roc” object, a list of class
“roc”. This object can be printed, plotted, or
passed to the functions pROC::roc(), pROC::ci(), pROC::smooth.roc()
and pROC::coords(). Additionally, two roc objects can be compared with pROC::roc.test().
This function is based on the roc function of R package pROC.
Usage
roc( pred, actual, auc = TRUE, smooth = FALSE, plot = FALSE, quiet = TRUE, ... )
Arguments
pred |
adjacency matrix (or a vector) corresponding to an estimated graph.
It can be an object with |
actual |
adjacency matrix (or a vector) corresponding to the actual graph structure in which |
smooth |
if TRUE, the ROC curve is passed to |
auc |
compute the area under the curve (AUC)? If |
plot |
plot the ROC curve? If |
quiet |
if |
... |
further arguments to be passed to |
Value
If the data contained any NA value and na.rm=FALSE, NA is
returned. Otherwise, if smooth=FALSE, a list of class
“roc” with the following fields:
auc |
if called with |
ci |
if called with |
response |
the response vector. Patients whose response is not
|
predictor |
predictor vector converted to numeric as used to build the ROC
curve. Patients whose response is not |
original.predictor, original.response |
response and predictor vectors as passed in argument. |
levels |
levels of the response as defined in argument. |
controls |
predictor values for the control observations. |
cases |
predictor values for the cases. |
percent |
if the sensitivities, specificities and AUC are reported in percent, as defined in argument. |
direction |
direction of the comparison, as defined in argument. |
fun.sesp |
function used to compute sensitivities and specificities. Will be re-used in bootstrap operations. |
sensitivities |
sensitivities defining the ROC curve. |
specificities |
specificities defining the ROC curve. |
thresholds |
thresholds at which the sensitivities and specificities were computed. See below for details. |
call |
how the function was called. See function |
If smooth=TRUE a list of class “smooth.roc” as returned
by pROC::smooth(), with or without additional elements
auc and ci (according to the call).
Author(s)
Reza Mohammadi a.mohammadi@uva.nl; Lucas Vogels l.f.o.vogels@uva.nl
References
Tom Fawcett (2006) “An introduction to ROC analysis”. Pattern Recognition Letters 27, 861–874, doi:10.1016/j.patrec.2005.10.010
Xavier Robin, Natacha Turck, Alexandre Hainard, et al. (2011) “pROC: an open-source package for R and S+ to analyze and compare ROC curves”. BMC Bioinformatics, 7, 77, doi:10.1186/1471-2105-12-77.
See Also
plotroc, pROC::plot.roc(), pROC::auc(), pROC::print.roc(), bdgraph, bdgraph.mpl, compare
Examples
## Not run:
set.seed( 5 )
# Generating multivariate normal data from a 'scale-free' graph
data.sim = bdgraph.sim( n = 200, p = 15, graph = "scale-free", vis = TRUE )
# Running BDMCMC algorithm
sample.bdmcmc = bdgraph( data = data.sim, algorithm = "bdmcmc", iter = 10000 )
# ROC curve for BDMCMC algorithm
roc.bdmcmc = BDgraph::roc( pred = sample.bdmcmc, actual = data.sim, plot = TRUE )
# Running RJMCMC algorithm
sample.rjmcmc = bdgraph( data = data.sim, algorithm = "rjmcmc", iter = 10000 )
# ROC curve for RJMCMC algorithm
roc.rjmcmc = BDgraph::roc( pred = sample.rjmcmc, actual = data.sim, plot = TRUE )
# ROC curve for both BDMCMC and RJMCMC algorithms
pROC::ggroc( list( BDMCMC = roc.bdmcmc, RJMCMC = roc.rjmcmc ) )
## End(Not run)
Sampling from Wishart distribution
Description
Generates random matrices, distributed according to the Wishart distribution with parameters b and D, W(b, D).
Usage
rwish( n = 1, p = 2, b = 3, D = diag( p ) ) Arguments
n |
number of samples required. |
p |
number of variables (nodes). |
b |
degree of freedom for Wishart distribution, |
D |
positive definite |
Details
Sampling from Wishart distribution, K \sim W(b, D), with density:
Pr(K) \propto |K| ^ {(b - 2) / 2} \exp \left\{- \frac{1}{2} \mbox{trace}(K \times D)\right\},
which b > 2 is the degree of freedom and D is a symmetric positive definite matrix.
Value
A numeric array, say A, of dimension (p \times p \times n), where each A[,,i] is a positive
definite matrix, a realization of the Wishart distribution W(b, D).
Note, for the case n=1, the output is a matrix.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
References
Lenkoski, A. (2013). A direct sampler for G-Wishart variates, Stat, 2:119-128, doi:10.1002/sta4.23
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, doi:10.18637/jss.v089.i03
See Also
Examples
sample <- rwish( n = 3, p = 5, b = 3, D = diag( 5 ) )
round( sample, 2 )
Graph selection
Description
Provides the selected graph which, based on input, could be a graph with links for which their estimated posterior probabilities are greater than 0.5 (default) or a graph with the highest posterior probability; see examples.
Usage
select( bdgraph.obj, cut = NULL, vis = FALSE ) Arguments
bdgraph.obj |
matrix in which each element response to the weight of the links.
It can be an object of |
cut |
threshold for including the links in the selected graph based on the estimated posterior probabilities of the links; see the examples. |
vis |
visualize the selected graph structure. |
Value
An adjacency matrix corresponding to the selected graph.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl 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, 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, 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, doi:10.1080/01621459.2021.1996377
Dobra, A. and Mohammadi, R. (2018). Loglinear Model Selection and Human Mobility, Annals of Applied Statistics, 12(2):815-845, doi:10.1214/18-AOAS1164
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, doi:10.1111/rssc.12171
See Also
Examples
## Not run:
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 50, p = 6, size = 7, vis = TRUE )
bdgraph.obj <- bdgraph( data = data.sim )
select( bdgraph.obj )
bdgraph.obj <- bdgraph( data = data.sim, save = TRUE )
select( bdgraph.obj )
select( bdgraph.obj, cut = 0.5, vis = TRUE )
## End(Not run)
Compute the sparsity of a graph
Description
Compute the sparsity of a graph/network or an object of calss "graph" from function graph.sim or an object of calss "sim" from function bdgraph.sim.
Usage
sparsity( adj ) Arguments
adj |
adjacency matrix corresponding to a graph structure in which |
Value
value corresponding to the graph sparsity which is the proportion of the non-links (non-zero elements) in adj.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl
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, doi:10.18637/jss.v089.i03
See Also
Examples
# Generating a 'random' graph
adj <- graph.sim( p = 10, graph = "random", prob = 0.4, vis = TRUE )
sparsity( adj )
Summary function for S3 class "bdgraph"
Description
Provides a summary of the results for function bdgraph.
Usage
## S3 method for class 'bdgraph'
summary( object, round = 2, vis = TRUE, ... )
Arguments
object |
object of |
round |
value for rounding all probabilities to the specified number of decimal places. |
vis |
visualize the results. |
... |
additional plotting parameters for the case |
Value
selected_g |
adjacency matrix corresponding to the selected graph which has the highest posterior probability. |
p_links |
upper triangular matrix corresponding to the posterior probabilities of all possible links. |
K_hat |
estimated precision matrix. |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl 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, doi:10.18637/jss.v089.i03
See Also
Examples
## Not run:
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 50, p = 6, size = 7, vis = TRUE )
bdgraph.obj <- bdgraph( data = data.sim )
summary( bdgraph.obj )
bdgraph.obj <- bdgraph( data = data.sim, save = TRUE )
summary( bdgraph.obj )
summary( bdgraph.obj, vis = FALSE )
## End(Not run)
Labor force survey data
Description
The survey dataset concerns 1002 males in the U.S labor force, described by Hoff (2007). The seven observed variables which have been measured on various scales are as follow: the income (income), degree (degree), the number of children (children), parents income (pincome), parents degree (pdegree), number of parents children (pchildren), and age (age).
Usage
data( surveyData ) Format
The format is a matrix with 1002 rows (number of individuals) and 7 column (number of variables).
References
Hoff, P. (2007). Extending the rank likelihood for semiparametric copula estimation, The Annals of Applied Statistics, 1(1), 265-283.
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, doi:10.18637/jss.v089.i03
Examples
data( surveyData )
summary( surveyData )
Trace plot of graph size
Description
Trace plot for graph size for the objects of S3 class "bdgraph", from function bdgraph.
It is a tool for monitoring the convergence of the sampling algorithms, BDMCMC and RJMCMC.
Usage
traceplot ( bdgraph.obj, acf = FALSE, pacf = FALSE, main = NULL, ... ) Arguments
bdgraph.obj |
object of |
acf |
visualize the autocorrelation functions for graph size. |
pacf |
visualize the partial autocorrelations for graph size. |
main |
graphical parameter (see plot). |
... |
system reserved (no specific usage). |
Author(s)
Reza Mohammadi a.mohammadi@uva.nl 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, 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, doi:10.1214/14-BA889
Dobra, A. and Mohammadi, R. (2018). Loglinear Model Selection and Human Mobility, Annals of Applied Statistics, 12(2):815-845, doi:10.1214/18-AOAS1164
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, doi:10.1111/rssc.12171
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
plotcoda, bdgraph, bdgraph.mpl
Examples
## Not run:
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 50, p = 6, size = 7, vis = TRUE )
bdgraph.obj <- bdgraph( data = data.sim, iter = 10000, burnin = 0, save = TRUE )
traceplot( bdgraph.obj )
traceplot( bdgraph.obj, acf = TRUE, pacf = TRUE )
## End(Not run)
transfer for count data
Description
Transfers count data, by counting the duplicated rows.
Usage
transfer( r_data ) Arguments
r_data |
( |
Value
(n \times p+1) matrix of transferred data, in which the last column is the frequency of duplicated rows.
Author(s)
Reza Mohammadi a.mohammadi@uva.nl and Adrian Dobra
References
Mohammadi, A. and Dobra, A. (2017). The R Package BDgraph for Bayesian Structure Learning in Graphical Models, ISBA Bulletin, 24(4):11-16
Dobra, A. and Mohammadi, R. (2018). Loglinear Model Selection and Human Mobility, Annals of Applied Statistics, 12(2):815-845, doi:10.1214/18-AOAS1164
See Also
Examples
# Generating multivariate binary data from a 'random' graph
data.sim <- bdgraph.sim( n = 12, p = 4, size = 4, type = "binary" )
r_data <- data.sim $ data
r_data
# Transfer the data
transfer( r_data )