Package 'GlarmaVarSel'

Variable Selection in Sparse GLARMA Models

Description

GlarmaVarSel consists of four functions: "variable_selection.R", "grad_hess_beta.R", "grad_hess_gamma.R" and "NR_gamma.R" For further information on how to use these functions, we refer the reader to the vignette of the package.

Details

GlarmaVarSel consists of four functions: "variable_selection.R", "grad_hess_beta.R", "grad_hess_gamma.R" and "NR_gamma.R" For further information on how to use these functions, we refer the reader to the vignette of the package.

Author(s)

Marina Gomtsyan, Celine Levy-Leduc, Sarah Ouadah, Laure Sansonnet

Maintainer: Marina Gomtsyan <[email protected]>

References

M. Gomtsyan et al. "Variable selection in sparse GLARMA models", arXiv:2007.08623v1

Examples

n=50
p=30
X = matrix(NA,(p+1),n)
f = 1/0.7
for(t in 1:n){X[,t]<-c(1,cos(2*pi*(1:(p/2))*t*f/n),sin(2*pi*(1:(p/2))*t*f/n))}
gamma0 = c(0)
data(Y)
result = variable_selection(Y, X, gamma0, k_max=2, n_iter=100, method="min",
nb_rep_ss=1000, threshold=0.7, parallel=FALSE, nb.cores=1)
beta_est = result$beta_est
Estim_active = result$estim_active
gamma_est = result$gamma_est

---

Gradient and Hessian of the log-likelihood with respect to beta

Description

This function calculates the gradient and Hessian of the log-likelihood with respect to beta.

Usage

grad_hess_beta(Y, X, beta0, gamma0)

Arguments

Y	Observation matrix
X	Design matrix
beta0	Initial beta vector
gamma0	Initial gamma vector

Value

grad_L_beta	Vector of the gradient of L with respect to beta
hess_L_beta	Matrix of the Hessian of L with respect to beta

Author(s)

Marina Gomtsyan, Celine Levy-Leduc, Sarah Ouadah, Laure Sansonnet

Maintainer: Marina Gomtsyan <[email protected]>

References

M. Gomtsyan et al. "Variable selection in sparse GLARMA models", arXiv:2007.08623v1

Examples

n=50
p=30
X = matrix(NA,(p+1),n)
f = 1/0.7
for(t in 1:n){X[,t]<-c(1,cos(2*pi*(1:(p/2))*t*f/n),sin(2*pi*(1:(p/2))*t*f/n))}
gamma0 = c(0)
data(Y)
glm_pois<-glm(Y~t(X)[,2:(p+1)],family = poisson)
beta0<-as.numeric(glm_pois$coefficients)
result = grad_hess_beta(Y, X, beta0, gamma0)
grad = result$grad_L_beta
Hessian = result$hess_L_beta

---

Gradient and Hessian of the log-likelihood with respect to gamma

Description

This function calculates the gradient and Hessian of the log-likelihood with respect to gamma

Usage

grad_hess_gamma(Y, X, beta0, gamma0)

Arguments

Y	Observation matrix
X	Design matrix
beta0	Initial beta vector
gamma0	Initial gamma vector

Value

grad_L_gamma	Vector of the gradient of L with respect to gamma
hess_L_gamma	Matrix of the Hessian of L with respect to gamma

Author(s)

Marina Gomtsyan, Celine Levy-Leduc, Sarah Ouadah, Laure Sansonnet

Maintainer: Marina Gomtsyan <[email protected]>

References

M. Gomtsyan et al. "Variable selection in sparse GLARMA models", arXiv:2007.08623v1

Examples

n=50
p=30
X = matrix(NA,(p+1),n)
f = 1/0.7
for(t in 1:n){X[,t]<-c(1,cos(2*pi*(1:(p/2))*t*f/n),sin(2*pi*(1:(p/2))*t*f/n))}
gamma0 = c(0)
data(Y)
glm_pois<-glm(Y~t(X)[,2:(p+1)],family = poisson)
beta0<-as.numeric(glm_pois$coefficients) 
result = grad_hess_gamma(Y, X, beta0, gamma0)
grad = result$grad_L_gamma
Hessian = result$hess_L_gamma

---

Newton-Raphson method for estimation of gamma

Description

This function estimates gamma with Newton-Raphson method

Usage

NR_gamma(Y, X, beta0, gamma0, n_iter)

Arguments

Y	Observation matrix
X	Design matrix
beta0	Initial beta vector
gamma0	Initial gamma vector
n_iter	Number of iterations of the algorithm. Default=100

Value

gamma

Estimated gamma vector

Author(s)

Marina Gomtsyan, Celine Levy-Leduc, Sarah Ouadah, Laure Sansonnet

Maintainer: Marina Gomtsyan <[email protected]>

References

M. Gomtsyan et al. "Variable selection in sparse GLARMA models", arXiv:2007.08623v1

Examples

n=50
p=30
X = matrix(NA,(p+1),n)
f = 1/0.7
for(t in 1:n){X[,t]<-c(1,cos(2*pi*(1:(p/2))*t*f/n),sin(2*pi*(1:(p/2))*t*f/n))}
gamma0 = c(0)
data(Y)
glm_pois<-glm(Y~t(X)[,2:(p+1)],family = poisson)
beta0<-as.numeric(glm_pois$coefficients)
gamma_est = NR_gamma(Y, X, beta0, gamma0, n_iter=100)

---

Variable selection

Description

This function performs variable selection, estimates a new vector beta and a new vector gamma

Usage

variable_selection(Y, X, gamma0, k_max = 2, n_iter = 100, method = "min", 
  nb_rep_ss = 1000, threshold = 0.8, parallel = FALSE, nb.cores = 1)

Arguments

Y	Observation matrix
X	Design matrix
gamma0	Initial gamma vector
k_max	Number of iteration to repeat the whole algorithm
n_iter	Number of iteration for Newton-Raphson algorithm
method	Stability selection method: "fast", "min" or "cv". In "min" the smallest lambda is chosen, in "cv" cross-validation lambda is chosen for stability selection. "fast" is a fater stability selection approach. The default is "min"
nb_rep_ss	Number of replications in stability selection step. The default is 1000
threshold	Threshold for stability selection. The default is 0.9
parallel	Whether to parallelize stability selection step or not. The default is FALSE
nb.cores	Number of cores for parallelization. The default is 1

Value

estim_active	Estimated active coefficients
beta_est	Vector of estimated beta values
gamma_est	Vector of estimated gamma values

Author(s)

Marina Gomtsyan, Celine Levy-Leduc, Sarah Ouadah, Laure Sansonnet

Maintainer: Marina Gomtsyan <[email protected]>

References

M. Gomtsyan et al. "Variable selection in sparse GLARMA models", arXiv:2007.08623v1

Examples

n=50
p=30
X = matrix(NA,(p+1),n)
f = 1/0.7
for(t in 1:n){X[,t]<-c(1,cos(2*pi*(1:(p/2))*t*f/n),sin(2*pi*(1:(p/2))*t*f/n))}
gamma0 = c(0)
data(Y)
result = variable_selection(Y, X, gamma0, k_max=2, n_iter=100, method="min",
nb_rep_ss=1000, threshold=0.7, parallel=FALSE, nb.cores=1)
beta_est = result$beta_est
Estim_active = result$estim_active
gamma_est = result$gamma_est

---

Observation matrix Y

Description

An example of observation matrix

Usage

data("Y")

Format

The format is: num [1:50] 11 8 3 3 3 4 4 4 3 1 ...

References

M. Gomtsyan et al. "Variable selection in sparse GLARMA models", arXiv:2007.08623v1

Examples

data(Y)

---