| Type: | Package |
| Title: | Multivariate Bayesian Sparse Group Selection with Spike and Slab |
| Version: | 1.1.0 |
| Author: | Benoit Liquet, Matthew Sutton |
| Maintainer: | Benoit Liquet <benoit.liquet@qut.edu.au> |
| Imports: | MCMCpack, MASS, mgcv, mnormt, truncnorm |
| Description: | An implementation of a Bayesian sparse group model using spike and slab priors in a regression context. It is designed for regression with a multivariate response variable, but also provides an implementation for univariate response. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2.0)] |
| Encoding: | UTF-8 |
| NeedsCompilation: | no |
| Packaged: | 2017-08-09 06:23:21 UTC; liquetwe |
| Repository: | CRAN |
| Date/Publication: | 2017-08-09 08:06:21 UTC |
Bayesian Group Lasso with Spike and Slab prior
Description
Run a gibbs sampler for a Bayesian group lasso model with spike and slab prior. This function is designed for an univariate response model and when the design matrix has a group structur. Run a gibbs sampler for a Bayesian group lasso model with spike and slab prior. This function is designed for an univariate response model and when the design matrix has a group structure.
Usage
BGLSS(Y, X, niter = 10000, burnin = 5000, group_size, a = 1,
b = 1, num_update = 100, niter.update = 100, verbose = FALSE,
alpha = 0.1, gamma = 0.1, pi_prior = TRUE, pi = 0.5,
update_tau = TRUE, option.weight.group = FALSE,
option.update = "global", lambda2_update = NULL)
Arguments
Y |
A numerical vector representing the univariate response variable. |
X |
A matrix respresenting the design matrix of the linear regression model. |
niter |
Number of iteration for the Gibbs sampler. |
burnin |
Number of burnin iteration |
group_size |
Integer vector representing the size of the groups of the design matrix |
a |
First shape parameter of the conjugate beta prior for |
b |
Second shape parameter of the conjugate beta prior for |
num_update |
Number of update regarding the scaling of the shrinkage parameter lambda which is calibrated by a Monte Carlo EM algorithm |
niter.update |
Number of itertion regarding the scaling of the shrinkage parameter lambda which is calibrated by a Monte Carlo EM algorithm |
verbose |
Logical. If "TRUE" iterations are displayed. |
alpha |
Shape parameter of the Inverse Gamma prior on the variance of the noise for the linear regression model. |
gamma |
Scale parameter of the Inverse Gamma prior on the variance of the noise for the linear regression model. |
pi_prior |
Logical. If "TRUE" a beta prior is used for pi |
pi |
Initial value for pi_0 which will be updated if |
update_tau |
Logical. If "TRUE" then a Monte Carlo EM algorithm is used to update lambda |
option.weight.group |
If "TRUE" then the group size is used for shrinkage penalty purpose. |
option.update |
Two options are proposed for updating lambda. A "Local" update or a "Global" update |
lambda2_update |
Value of the square of lambda when |
Value
BGLSS returns a list that contains the following components:
pos_mean |
The posterior mean estimate of the regression coefficients |
pos_median |
The posterior mean estimate of the regression coefficients |
coef |
A matrix with the regression coefficients sampled at each iteration |
Author(s)
Benoit Liquet, Matthew Sutton and Xiaofan Xu.
References
B. Liquet, K. Mengersen, A. Pettitt and M. Sutton. (2016). Bayesian Variable Selection Regression Of Multivariate Responses For Group Data. Submitted in Bayesian Analysis.
Xu, X. and Ghosh, M. (2015). Bayesian Variable Selection and Estimation for Group Lasso. Bayesian Analysis, 10(4): 909–936.
See Also
Examples
## Simulation of datasets X and Y with group variables
set.seed(1)
data1 = gen_data_uni(nsample = 120,cor.var=0.5, ntrain = 80)
data1 = normalize(data1)
true_model <- data1$true_model
X <- data1$X
Y<- data1$Y
train_idx <- data1$train_idx
gsize <- data1$gsize
## We recommend to set niter=50000, burnin=10000
## num_update = 100 and niter.update = 100
## to reach convergence
model <- BGLSS(Y[,1],X,niter=500,burnin=100,group_size=gsize,
num_update = 20,niter.update = 20)
model$pos_median!=0
true_model
Bayesian Sparse Group Selection with Spike and Slab priors
Description
Run a gibbs sampler for a Bayesian sparse group selection model with spike and slab priors. This function is designed for an univariate response model and when the design matrix has a group structure.
Usage
BSGSSS(Y, X, group_size, niter = 10000, burnin = 5000,
pi0 = 0.5, pi1 = 0.5, num_update = 100, niter.update = 100,
alpha = 0.1, gamma = 0.1, a1 = 1, a2 = 1, c1 = 1, c2 = 1,
pi_prior = TRUE)
Arguments
Y |
A numerical vector representing the univariate response variable. |
X |
A matrix respresenting the design matrix of the linear regression model. |
group_size |
Integer vector representing the size of the groups of the design matrix |
niter |
Number of iteration for the Gibbs sampler. |
burnin |
Number of burnin iteration |
pi0 |
Initial value for pi0 which will be updated if |
pi1 |
Initial value for pi1 which will be updated if |
num_update |
Number of update regarding the scaling of the shrinkage parameter lambda which is calibrated by a Monte Carlo EM algorithm |
niter.update |
Number of itertion regarding the scaling of the shrinkage parameter lambda which is calibrated by a Monte Carlo EM algorithm |
alpha |
Shape parameter of the Inverse Gamma prior on the variance of the noise for the linear regression model. |
gamma |
Scale parameter of the Inverse Gamma prior on the variance of the noise for the linear regression model. |
a1 |
First shape parameter of the conjugate beta hyper-prior for |
a2 |
Second shape parameter of the conjugate beta prior for |
c1 |
First shape parameter of the conjugate beta hyper-prior for |
c2 |
Second shape parameter of the conjugate beta prior for |
pi_prior |
Logical. If "TRUE" beta priors are used for pi0 and pi1 |
Value
BSGSSS returns a list that contains the following components:
pos_mean |
The posterior mean estimate of the regression coefficients |
pos_median |
The posterior mean estimate of the regression coefficients |
coef |
A matrix with the regression coefficients sampled at each iteration |
Author(s)
Benoit Liquet, Matthew Sutton and Xiaofan Xu.
References
B. Liquet, K. Mengersen, A. Pettitt and M. Sutton. (2016). Bayesian Variable Selection Regression Of Multivariate Responses For Group Data. Submitted in Bayesian Analysis.
Xu, X. and Ghosh, M. (2015). Bayesian Variable Selection and Estimation for Group Lasso. Bayesian Analysis, 10(4): 909–936.
See Also
Examples
## Simulation of datasets X and Y with group variables
set.seed(1)
data1 = gen_data_uni(nsample = 120,cor.var=0.5, ntrain = 80)
data1 = normalize(data1)
true_model <- data1$true_model
X <- data1$X
Y<- data1$Y
train_idx <- data1$train_idx
gsize <- data1$gsize
## We recommend to set niter=50000, burnin=10000
## num_update = 100 and niter.update = 100
## to reach convergence
model <- BSGSSS(Y[,1],X,niter=500,burnin=100,group_size=gsize,
num_update = 20,niter.update = 20)
model$pos_median!=0
true_model
Multivariate Bayesian Group Lasso with Spike and Slab prior
Description
Run a gibbs sampler for a Multivariate Bayesian group lasso model with spike and slab prior. This function is designed for a regression model with multivariate response, where the design matrix has a group structure.
Usage
MBGLSS(Y, X, niter = 10000, burnin = 5000, group_size,
a = 1, b = 1, num_update = 100, niter.update = 100,
verbose = FALSE, pi_prior = TRUE, pi = 0.5,
d = 3, update_tau = TRUE, option.update = "global")
Arguments
Y |
A numerical vector representing the univariate response variable. |
X |
A matrix respresenting the design matrix of the linear regression model. |
niter |
Number of iteration for the Gibbs sampler. |
burnin |
Number of burnin iteration |
group_size |
Integer vector representing the size of the groups of the design matrix |
a |
First shape parameter of the conjugate beta prior for |
b |
Second shape parameter of the conjugate beta prior for |
num_update |
Number of update regarding the scaling of the shrinkage parameter lambda which is calibrated by a Monte Carlo EM algorithm |
niter.update |
Number of itertion regarding the scaling of the shrinkage parameter lambda which is calibrated by a Monte Carlo EM algorithm |
verbose |
Logical. If "TRUE" iterations are displayed. |
pi_prior |
Logical. If "TRUE" a beta prior is used for pi |
pi |
Initial value for pi_0 which will be updated if |
d |
Degree of freedom of the inverse Wishart prior of the covariance matrix of the response variable. By default |
update_tau |
Logical. If "TRUE" then a Monte Carlo EM algorithm is used to update lambda |
option.update |
Two options are proposed for updating lambda. A "Local" update or a "Global" update |
Value
BSGSSS returns a list that contains the following components:
pos_mean |
The posterior mean estimate of the regression coefficients |
pos_median |
The posterior mean estimate of the regression coefficients |
coef |
A matrix with the regression coefficients sampled at each iteration |
Author(s)
Benoit Liquet and Matthew Sutton.
References
B. Liquet, K. Mengersen, A. Pettitt and M. Sutton. (2016). Bayesian Variable Selection Regression Of Multivariate Responses For Group Data. Submitted in Bayesian Analysis.
See Also
Examples
## Not run:
## Simulation of datasets X and Y with group variables
data1 = gen_data_Multi(nsample = 120, ntrain = 80)
data1 = Mnormalize(data1)
true_model <- data1$true_model
X <- data1$X
Y<- data1$Y
train_idx <- data1$train_idx
gsize <- data1$gsize
niter <- 2000
burnin <- 1000
model <- MBGLSS(Y,X,niter,burnin,gsize,num_update = 100,
niter.update = 100)
model$pos_median[,1]!=0
## End(Not run)Internal Functions
Description
Internal functions not to be used by the user.
Multivariate Bayesian Sparse Group Selection with Spike and Slab priors
Description
Run a gibbs sampler for a Multivariate Bayesian sparse group selection model with spike and slab prior. This function is designed for a regression model with multivariate response, where the design matrix has a group structure.
Usage
MBSGSSS(Y, X, group_size, pi0 = 0.5, pi1 = 0.5,
a1 = 1, a2 = 1, c1 = 1,c2 = 1, pi_prior = TRUE,
niter = 10000, burnin = 5000, d = 3,
num_update = 100, niter.update = 100)
Arguments
Y |
A numerical vector representing the univariate response variable. |
X |
A matrix respresenting the design matrix of the linear regression model. |
group_size |
Integer vector representing the size of the groups of the design matrix |
pi0 |
Initial value for pi0 which will be updated if |
pi1 |
Initial value for pi1 which will be updated if |
a1 |
First shape parameter of the conjugate beta hyper-prior for |
a2 |
Second shape parameter of the conjugate beta prior for |
c1 |
First shape parameter of the conjugate beta hyper-prior for |
c2 |
Second shape parameter of the conjugate beta prior for |
pi_prior |
Logical. If "TRUE" beta priors are used for pi0 and pi1 |
niter |
Number of iteration for the Gibbs sampler. |
burnin |
Number of burnin iteration |
d |
Degree of freedom of the inverse Wishart prior of the covariance matrix of the response variable. By default |
num_update |
Number of update regarding the scaling of the shrinkage parameter lambda which is calibrated by a Monte Carlo EM algorithm |
niter.update |
Number of itertion regarding the scaling of the shrinkage parameter lambda which is calibrated by a Monte Carlo EM algorithm |
Author(s)
Benoit Liquet and Matthew Sutton.
References
B. Liquet, K. Mengersen, A. Pettitt and M. Sutton. (2016). Bayesian Variable Selection Regression Of Multivariate Responses For Group Data. Submitted in Bayesian Analysis.
See Also
Examples
## Not run:
## Simulation of datasets X and Y with group variables
data1 = gen_data_Multi(nsample = 120, ntrain = 80)
data1 = Mnormalize(data1)
true_model <- data1$true_model
X <- data1$X
Y<- data1$Y
train_idx <- data1$train_idx
gsize <- data1$gsize
niter <- 2000
burnin <- 1000
model <- MBSGSSS(Y,X,niter=niter,burnin=burnin,group_size=gsize,
num_update = 50,niter.update = 50)
model$pos_median[,1]!=0
## End(Not run)