| Title: | Sliced Inverse Regression with Thresholding |
|---|---|
| Description: | Implements a thresholded version of the Sliced Inverse Regression method, which allows to do variable selection. |
| Authors: | Clement Weinreich [aut, cre], Jerome Saracco [aut], Hadrien Lorenzo [aut] |
| Maintainer: | Clement Weinreich <[email protected]> |
| License: | GPL (>=2.0) |
| Version: | 1.0.2 |
| Built: | 2025-02-20 05:00:07 UTC |
| Source: | https://github.com/clement-w/sirthresholded |
Display the 10 first eigen values and the estimated index versus Y of the SIR model.
## S3 method for class 'SIR' plot(x, choice = "", ...)## S3 method for class 'SIR' plot(x, choice = "", ...)
x |
A SIR object |
choice |
the graph to plot:
|
... |
arguments to be passed to methods, such as graphical parameters (not used here). |
No return value
# Generate Data set.seed(10) n <- 500 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply SIR res = SIR(Y, X, H = 10, graph = FALSE) # Eigen values plot(res,choice="eigvals") # Estimated index versus Y plot(res,choice="estim_ind")# Generate Data set.seed(10) n <- 500 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply SIR res = SIR(Y, X, H = 10, graph = FALSE) # Eigen values plot(res,choice="eigvals") # Estimated index versus Y plot(res,choice="estim_ind")
Display the 10 first eigen values and the estimated index versus Y of the SIRbootstrap model.
## S3 method for class 'SIR_bootstrap' plot(x, choice = "", ...)## S3 method for class 'SIR_bootstrap' plot(x, choice = "", ...)
x |
A SIR_bootstrap object |
choice |
the graph to plot:
|
... |
arguments to be passed to methods, such as graphical parameters (not used here). |
No return value
# Generate Data set.seed(10) n <- 500 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply bootstrap SIR res = SIR_bootstrap(Y, X, H = 10, B = 10) # Eigen values plot(res,choice="eigvals") # Estimated index versus Y plot(res,choice="estim_ind")# Generate Data set.seed(10) n <- 500 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply bootstrap SIR res = SIR_bootstrap(Y, X, H = 10, B = 10) # Eigen values plot(res,choice="eigvals") # Estimated index versus Y plot(res,choice="estim_ind")
Display the 10 first eigen values and the estimated index versus Y of the thresholded SIR model.
## S3 method for class 'SIR_threshold' plot(x, choice = "", ...)## S3 method for class 'SIR_threshold' plot(x, choice = "", ...)
x |
A SIR_threshold object |
choice |
the graph to plot:
|
... |
arguments to be passed to methods, such as graphical parameters (not used here). |
No return value
# Generate Data set.seed(10) n <- 500 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply SIR with hard thresholding res = SIR_threshold(Y, X, H = 10, lambda = 0.2, thresholding = "hard") # Eigen values plot(res,choice="eigvals") # Estimated index versus Y plot(res,choice="estim_ind")# Generate Data set.seed(10) n <- 500 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply SIR with hard thresholding res = SIR_threshold(Y, X, H = 10, lambda = 0.2, thresholding = "hard") # Eigen values plot(res,choice="eigvals") # Estimated index versus Y plot(res,choice="estim_ind")
Display the estimated index versus Y of the SIR model, the size of the models,
the occurrence of variable selection, the distribution of the coefficients of
and and the distribution of found across the replications.
## S3 method for class 'SIR_threshold_bootstrap' plot(x, choice = "", ...)## S3 method for class 'SIR_threshold_bootstrap' plot(x, choice = "", ...)
x |
A SIR_threshold_bootstrap object |
choice |
the graph to plot:
|
... |
arguments to be passed to methods, such as graphical parameters (not used here). |
No return value
# Generate Data set.seed(10) n <- 200 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps res = SIR_threshold_bootstrap(Y,X,H=10,n_lambda=300,thresholding="hard", n_replications=30,k=2) # Estimated index versus Y plot(res,choice="estim_ind") # Model size plot(res,choice="size") # Selected variables plot(res,choice="selec_var") # Coefficients of b plot(res,choice="coefs_b") # Optimal lambdas plot(res,choice="lambdas_replic")# Generate Data set.seed(10) n <- 200 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps res = SIR_threshold_bootstrap(Y,X,H=10,n_lambda=300,thresholding="hard", n_replications=30,k=2) # Estimated index versus Y plot(res,choice="estim_ind") # Model size plot(res,choice="size") # Selected variables plot(res,choice="selec_var") # Coefficients of b plot(res,choice="coefs_b") # Optimal lambdas plot(res,choice="lambdas_replic")
Display the 10 first eigen values,the estimated index versus Y of the SIR model,
the evolution of and variable selection according to , and the
regularization path of .
## S3 method for class 'SIR_threshold_opt' plot(x, choice = "", ...)## S3 method for class 'SIR_threshold_opt' plot(x, choice = "", ...)
x |
A SIR_threshold_opt object |
choice |
the graph to plot:
|
... |
arguments to be passed to methods, such as graphical parameters (not used here). |
No return value
# Generate Data set.seed(10) n <- 200 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply SIR with soft thresholding res = SIR_threshold_opt(Y,X,H=10,n_lambda=100,thresholding="soft") # Estimated index versus Y plot(res,choice="estim_ind") # Choice of optimal lambda plot(res,choice="opt_lambda") # Evolution of cos^2 and var selection according to lambda plot(res,choice="cos2_selec") # Regularization path plot(res,choice="regul_path")# Generate Data set.seed(10) n <- 200 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply SIR with soft thresholding res = SIR_threshold_opt(Y,X,H=10,n_lambda=100,thresholding="soft") # Estimated index versus Y plot(res,choice="estim_ind") # Choice of optimal lambda plot(res,choice="opt_lambda") # Evolution of cos^2 and var selection according to lambda plot(res,choice="cos2_selec") # Regularization path plot(res,choice="regul_path")
Apply a single-index on with slices. This function allows to obtain an
estimate of a basis of the (Effective Dimension Reduction) space via the eigenvector
associated with the largest nonzero eigenvalue of the matrix of interest
. Thus, is an direction.
SIR(Y, X, H = 10, graph = TRUE, choice = "")SIR(Y, X, H = 10, graph = TRUE, choice = "")
Y |
A numeric vector representing the dependent variable (a response vector). |
X |
A matrix representing the quantitative explanatory variables (bind by column). |
H |
The chosen number of slices (default is 10). |
graph |
A boolean that must be set to true to display graphics (default is TRUE). |
choice |
the graph to plot:
|
An object of class SIR, with attributes:
b |
This is an estimated EDR direction, which is the principal eigenvector of the interest matrix. |
M1 |
The interest matrix. |
eig_val |
The eigenvalues of the interest matrix. |
n |
Sample size. |
p |
The number of variables in X. |
H |
The chosen number of slices. |
call |
Unevaluated call to the function. |
index_pred |
The index Xb' estimated by SIR. |
Y |
The response vector. |
# Generate Data set.seed(10) n <- 500 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply SIR SIR(Y, X, H = 10)# Generate Data set.seed(10) n <- 500 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply SIR SIR(Y, X, H = 10)
Apply a single-index on bootstraped samples of with slices.
SIR_bootstrap(Y, X, H = 10, B = 10, graph = TRUE, choice = "")SIR_bootstrap(Y, X, H = 10, B = 10, graph = TRUE, choice = "")
Y |
A numeric vector representing the dependent variable (a response vector). |
X |
A matrix representing the quantitative explanatory variables (bind by column). |
H |
The chosen number of slices (default is 10). |
B |
The number of bootstrapped samples to draw (default is 10). |
graph |
A boolean that must be set to true to display graphics (default is TRUE). |
choice |
the graph to plot:
|
An object of class SIR_bootstrap, with attributes:
b |
This is an estimated EDR direction, which is the principal eigenvector of the interest matrix. |
mat_b |
A matrix of size p*B that contains an estimation of beta in the columns for each bootstrapped sample. |
n |
Sample size. |
p |
The number of variables in X. |
H |
The chosen number of slices. |
call |
Unevaluated call to the function. |
index_pred |
The index b'X estimated by SIR. |
Y |
The response vector. |
# Generate Data set.seed(10) n <- 500 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply bootstrap SIR SIR_bootstrap(Y, X, H = 10, B = 10)# Generate Data set.seed(10) n <- 500 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply bootstrap SIR SIR_bootstrap(Y, X, H = 10, B = 10)
Apply a single-index on with slices, with a parameter which
apply a soft/hard thresholding to the interest matrix .
SIR_threshold( Y, X, H = 10, lambda = 0, thresholding = "hard", graph = TRUE, choice = "" )SIR_threshold( Y, X, H = 10, lambda = 0, thresholding = "hard", graph = TRUE, choice = "" )
Y |
A numeric vector representing the dependent variable (a response vector). |
X |
A matrix representing the quantitative explanatory variables (bind by column). |
H |
The chosen number of slices (default is 10). |
lambda |
The thresholding parameter (default is 0). |
thresholding |
The thresholding method to choose between hard and soft (default is hard). |
graph |
A boolean that must be set to true to display graphics (default is TRUE). |
choice |
the graph to plot:
|
An object of class SIR_threshold, with attributes:
b |
This is an estimated EDR direction, which is the principal eigenvector of the interest matrix. |
M1 |
The interest matrix thresholded. |
eig_val |
The eigenvalues of the interest matrix thresholded. |
eig_vect |
A matrix corresponding to the eigenvectors of the interest matrix. |
Y |
The response vector. |
n |
Sample size. |
p |
The number of variables in X. |
H |
The chosen number of slices. |
nb.zeros |
The number of 0 in the estimation of the vector beta. |
index_pred |
The index Xb' estimated by SIR. |
list.relevant.variables |
A list that contains the variables selected by the model. |
cos_squared |
The cosine squared between vanilla SIR and SIR thresholded. |
lambda |
The thresholding parameter used. |
thresholding |
The thresholding method used. |
call |
Unevaluated call to the function. |
X_reduced |
The X data restricted to the variables selected by the model. It can be used to estimate a new SIR model on the relevant variables to improve the estimation of b. |
# Generate Data set.seed(10) n <- 500 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply SIR with hard thresholding SIR_threshold(Y, X, H = 10, lambda = 0.2, thresholding = "hard")# Generate Data set.seed(10) n <- 500 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply SIR with hard thresholding SIR_threshold(Y, X, H = 10, lambda = 0.2, thresholding = "hard")
Apply a single-index optimally soft/hard thresholded with slices on
'n_replications' bootstraped replications of . The optimal number of
selected variables is the number of selected variables that came back most often
among the replications performed. From this, we can get the corresponding
and that produce the same number of selected variables in the result of
'SIR_threshold_opt'.
SIR_threshold_bootstrap( Y, X, H = 10, thresholding = "hard", n_replications = 50, graph = TRUE, output = TRUE, n_lambda = 100, k = 2, choice = "" )SIR_threshold_bootstrap( Y, X, H = 10, thresholding = "hard", n_replications = 50, graph = TRUE, output = TRUE, n_lambda = 100, k = 2, choice = "" )
Y |
A numeric vector representing the dependent variable (a response vector). |
X |
A matrix representing the quantitative explanatory variables (bind by column). |
H |
The chosen number of slices (default is 10). |
thresholding |
The thresholding method to choose between hard and soft (default is hard). |
n_replications |
The number of bootstraped replications of (X,Y) done to estimate the model (default is 50). |
graph |
A boolean, set to TRUE to plot graphs (default is TRUE). |
output |
A boolean, set to TRUE to print information (default is TRUE). |
n_lambda |
The number of lambda to test. The n_lambda tested lambdas are uniformally distributed between 0 and the maximum value of the interest matrix (default is 100). |
k |
Multiplication factor of the bootstrapped sample size (default is 1 = keep the same size as original data). |
choice |
the graph to plot:
|
An object of class SIR_threshold_bootstrap, with attributes:
b |
This is the optimal estimated EDR direction, which is the principal eigenvector of the interest matrix. |
lambda_opt |
The optimal lambda. |
vec_nb_var_selec |
Vector that contains the number of selected variables for each replications. |
occurrences_var |
Vector that contains at index i the number of times the i_th variable has been selected in a replication. |
call |
Unevaluated call to the function. |
nb_var_selec_opt |
Optimal number of selected variables which is the number of selected variables that came back most often among the replications performed. |
list_relevant_variables |
A list that contains the variables selected by the model. |
n |
Sample size. |
p |
The number of variables in X. |
H |
The chosen number of slices. |
n_replications |
The number of bootstraped replications of (X,Y) done to estimate the model. |
thresholding |
The thresholding method used. |
X_reduced |
The X data restricted to the variables selected by the model. It can be used to estimate a new SIR model on the relevant variables to improve the estimation of b. |
mat_b |
Contains the estimation b at each bootstraped replications. |
lambdas_opt_boot |
Contains the optimal lambda found by SIR_threshold_opt at each replication. |
index_pred |
The index Xb' estimated by SIR. |
Y |
The response vector. |
M1 |
The interest matrix thresholded with the optimal lambda. |
# Generate Data set.seed(8) n <- 170 beta <- c(1,1,1,1,1,rep(0,15)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,20)) eps <- rnorm(n,sd=8) Y <- (X%*%beta)**3+eps # Apply SIR with hard thresholding SIR_threshold_bootstrap(Y,X,H=10,n_lambda=300,thresholding="hard", n_replications=30,k=2)# Generate Data set.seed(8) n <- 170 beta <- c(1,1,1,1,1,rep(0,15)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,20)) eps <- rnorm(n,sd=8) Y <- (X%*%beta)**3+eps # Apply SIR with hard thresholding SIR_threshold_bootstrap(Y,X,H=10,n_lambda=300,thresholding="hard", n_replications=30,k=2)
Apply a single-index on with slices, with a soft/hard thresholding
of the interest matrix by an optimal
parameter . The is found automatically among a vector
of n_lambda , starting from 0 to the maximum value of
. For each feature of ,
the number of associated with a selection of this feature is stored
(in a vector of size ). This vector is sorted in a decreasing way. Then, thanks to
strucchange::breakpoints, a breakpoint is found in this sorted vector. The coefficients
of the variables at the left of the breakpoint, tend to be automatically toggled to 0 due
to the thresholding operation based on , and so should be removed (useless
variables). Finally, corresponds to the first such that the
associated provides the same number of zeros as the breakpoint's value.
For example, for and n_lambda=100, this sorted vector can look like this :
| X10 | X3 | X8 | X5 | X7 | X9 | X4 | X6 | X2 | X1 |
| 2 | 3 | 3 | 4 | 4 | 4 | 6 | 10 | 95 | 100 |
Here, the breakpoint would be 8.
SIR_threshold_opt( Y, X, H = 10, n_lambda = 100, thresholding = "hard", graph = TRUE, output = TRUE, choice = "" )SIR_threshold_opt( Y, X, H = 10, n_lambda = 100, thresholding = "hard", graph = TRUE, output = TRUE, choice = "" )
Y |
A numeric vector representing the dependent variable (a response vector). |
X |
A matrix representing the quantitative explanatory variables (bind by column). |
H |
The chosen number of slices (default is 10). |
n_lambda |
The number of lambda to test. The n_lambda tested lambdas are uniformally distributed between 0 and the maximum value of the interest matrix. (default is 100). |
thresholding |
The thresholding method to choose between hard and soft (default is hard). |
graph |
A boolean, set to TRUE to plot graphs (default is TRUE). |
output |
A boolean, set to TRUE to print informations (default is TRUE). |
choice |
the graph to plot:
|
An object of class SIR_threshold_opt, with attributes:
b |
This is the optimal estimated EDR direction, which is the principal eigenvector of the interest matrix. |
lambdas |
A vector that contains the tested lambdas. |
lambda_opt |
The optimal lambda. |
mat_b |
A matrix of size p*n_lambda that contains an estimation of beta in the columns for each lambda. |
n_lambda |
The number of lambda tested. |
vect_nb_zeros |
The number of 0 in b for each lambda. |
list_relevant_variables |
A list that contains the variables selected by the model. |
fit_bp |
An object of class breakpoints from the strucchange package, that contains informations about the breakpoint which allows to deduce the optimal lambda. |
indices_useless_var |
A vector that contains p items: each variable is associated with the number of lambda that selects this variable. |
vect_cos_squared |
A vector that contains for each lambda, the cosine squared between vanilla SIR and SIR thresholded. |
Y |
The response vector. |
n |
Sample size. |
p |
The number of variables in X. |
H |
The chosen number of slices. |
M1 |
The interest matrix thresholded with the optimal lambda. |
thresholding |
The thresholding method used. |
call |
Unevaluated call to the function. |
X_reduced |
The X data restricted to the variables selected by the model. It can be used to estimate a new SIR model on the relevant variables to improve the estimation of b. |
index_pred |
The index Xb' estimated by SIR. |
# Generate Data set.seed(2) n <- 200 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply SIR with soft thresholding SIR_threshold_opt(Y,X,H=10,n_lambda=300,thresholding="soft")# Generate Data set.seed(2) n <- 200 beta <- c(1,1,rep(0,8)) X <- mvtnorm::rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta)**3+eps # Apply SIR with soft thresholding SIR_threshold_opt(Y,X,H=10,n_lambda=300,thresholding="soft")