Package 'tlars'

Toy data generated from a Gaussian linear model

Description

A data set containing a predictor matrix X with n = 50 observations and p = 100 variables (predictors), and a sparse parameter vector beta with associated support vector.

Usage

Gauss_data

Format

A list containing a matrix X and vectors y, beta, and support:

X

Predictor matrix, n = 50, p = 100.

y

Response vector.

beta

Parameter vector.

support

support vector.

Examples

# Generated as follows:
set.seed(789)
n <- 50
p <- 100
X <- matrix(stats::rnorm(n * p), nrow = n, ncol = p)
beta <- c(rep(5, times = 3), rep(0, times = 97))
support <- beta > 0
y <- X %*% beta + stats::rnorm(n)
Gauss_data <- list(
  X = X,
  y = y,
  beta = beta,
  support = support
)

---

Plots the T-LARS solution path

Description

Plots the T-LARS solution path stored in C++ objects of class tlars_cpp (see tlars_cpp for details) if the object is created with type = "lar" (no plot for type = "lasso").

Usage

## S3 method for class 'Rcpp_tlars_cpp'
plot(
  x,
  xlab = "# Included dummies",
  ylab = "Coefficients",
  include_dummies = TRUE,
  actions = TRUE,
  col_selected = "black",
  col_dummies = "red",
  lty_selected = "solid",
  lty_dummies = "dashed",
  legend_pos = "topleft",
  ...
)

Arguments

x	Object of the class tlars_cpp. See tlars_cpp for details.
xlab	Label of the x-axis.
ylab	Label of the y-axis.
include_dummies	Logical. If TRUE solution paths of dummies are added to the plot.
actions	Logical. If TRUE axis above plot with indices of added variables (Dummies represented by 'D') along the solution path is added.
col_selected	Color of lines corresponding to selected variables.
col_dummies	Color of lines corresponding to included dummies.
lty_selected	Line type of lines corresponding to selected variables. See par for more details.
lty_dummies	Line type of lines corresponding to included dummies. See par for more details.
legend_pos	Legend position. See xy.coords for more details.
...	Ignored. Only added to keep structure of generic plot function.

Value

Plots the T-LARS solution path stored in C++ objects of class tlars_cpp (no plot for type = "lasso").

See Also

tlars_cpp, plot, par, and xy.coords.

Examples

data("Gauss_data")
X <- Gauss_data$X
y <- drop(Gauss_data$y)
p <- ncol(X)
n <- nrow(X)
num_dummies <- p
dummies <- matrix(stats::rnorm(n * p), nrow = n, ncol = num_dummies)
XD <- cbind(X, dummies)
mod_tlars <- tlars_model(X = XD, y = y, num_dummies = num_dummies)
tlars(model = mod_tlars, T_stop = 3, early_stop = TRUE)
plot(mod_tlars)

---

Prints a summary of the results stored in a C++ object of class tlars_cpp.

Description

Prints a summary of the results stored in a C++ object of class tlars_cpp (see tlars_cpp for details), i.e., selected variables, computation time, and number of included dummies.

Usage

## S3 method for class 'Rcpp_tlars_cpp'
print(x, ...)

Arguments

x	Object of the class tlars_cpp. See tlars_cpp for details.
...	Ignored. Only added to keep structure of generic print function.

Value

Prints a summary of the results stored in a C++ object of class tlars_cpp.

See Also

tlars_cpp.

Examples

data("Gauss_data")
X <- Gauss_data$X
y <- drop(Gauss_data$y)
p <- ncol(X)
n <- nrow(X)
num_dummies <- p
dummies <- matrix(stats::rnorm(n * p), nrow = n, ncol = num_dummies)
XD <- cbind(X, dummies)
mod_tlars <- tlars_model(X = XD, y = y, num_dummies = num_dummies)
tlars(model = mod_tlars, T_stop = 3, early_stop = TRUE)
print(mod_tlars)

---

Executes the Terminating-LARS (T-LARS) algorithm

Description

Modifies the generic tlars_cpp model by executing the T-LARS algorithm and including the results in the tlars_cpp model.

Usage

tlars(model, T_stop = 1, early_stop = TRUE, info = TRUE)

Arguments

model	Object of the class tlars_cpp.
T_stop	Number of included dummies after which the random experiments (i.e., forward selection processes) are stopped.
early_stop	Logical. If TRUE, then the forward selection process is stopped after T_stop dummies have been included. Otherwise the entire solution path is computed.
info	If TRUE information about the T-LARS step are printed.

Value

No return value. Executes the T-LARS algorithm and includes the results in the associated object of class tlars_cpp.

Examples

data("Gauss_data")
X <- Gauss_data$X
y <- drop(Gauss_data$y)
p <- ncol(X)
n <- nrow(X)
num_dummies <- p
dummies <- matrix(stats::rnorm(n * p), nrow = n, ncol = num_dummies)
XD <- cbind(X, dummies)
mod_tlars <- tlars_model(X = XD, y = y, num_dummies = num_dummies)
tlars(model = mod_tlars, T_stop = 3, early_stop = TRUE)
beta <- mod_tlars$get_beta()
beta

---

Exposes the C++ class tlars_cpp to R

Description

Type 'tlars_cpp' in the console to see the constructors, variables, and methods of the class tlars_cpp.

Arguments

X	Real valued predictor matrix.
y	Response vector.
verbose	Logical. If TRUE progress in computations is shown.
intercept	Logical. If TRUE an intercept is included.
standardize	Logical. If TRUE the predictors are standardized and the response is centered.
num_dummies	Number of dummies that are appended to the predictor matrix.
type	Type of used algorithm (currently possible choices: 'lar' or 'lasso').
lars_state	Input list that was extracted from a previous tlars_cpp object using get_all().
T_stop	Number of included dummies after which the random experiments (i.e., forward selection processes) are stopped.
early_stop	Logical. If TRUE, then the forward selection process is stopped after T_stop dummies have been included. Otherwise the entire solution path is computed.

Value

No return value. Exposes the C++ class tlars_cpp to R.

Fields

Constructor:

new - Creates a new object of the class tlars_cpp.

Constructor:

new - Re-creates an object of the class tlars_cpp based on a list of class variables that is obtained via get_all().

Method:

execute_lars_step - Executes LARS steps until a stopping-condition is satisfied.

Method:

get_beta - Returns the estimate of the beta vector.

Method:

get_beta_path - Returns a a matrix with the estimates of the beta vectors at all steps.

Method:

get_num_active - Returns the number of active predictors.

Method:

get_num_active_dummies - Returns the number of dummy variables that have been included.

Method:

get_num_dummies - Returns the number of dummy predictors.

Method:

get_actions - Returns the indices of added/removed variables along the solution path.

Method:

get_df - Returns the degrees of freedom at each step which is given by number of active variables (+1 if intercept is true).

Method:

get_R2 - Returns the R^2 statistic at each step.

Method:

get_RSS - Returns the residual sum of squares at each step.

Method:

get_Cp - Returns the Cp-statistic at each step.

Method:

get_lambda - Returns the lambda-values (penalty parameters) at each step along the solution path.

Method:

get_entry - Returns the first entry/selection steps of the predictors along the solution path.

Method:

get_norm_X - Returns the L2-norm of the predictors.

Method:

get_mean_X - Returns the sample means of the predictors.

Method:

get_mean_y - Returns the sample mean of the response y.

Method:

get_all - Returns all class variables: This list can be used as an input to the constructor to re-create an object of class tlars_cpp.

Examples

data("Gauss_data")
X <- Gauss_data$X
y <- drop(Gauss_data$y)
p <- ncol(X)
n <- nrow(X)
dummies <- matrix(stats::rnorm(n * p), nrow = n, ncol = p)
XD <- cbind(X, dummies)
mod_tlars <- tlars_model(X = XD, y = y, num_dummies = ncol(dummies))
tlars(model = mod_tlars, T_stop = 3, early_stop = TRUE)

mod_tlars$get_beta()

# mod_tlars$get_beta_path()
# mod_tlars$get_num_active()
# mod_tlars$get_num_active_dummies()
# mod_tlars$get_num_dummies()
# mod_tlars$get_actions()
# mod_tlars$get_df()
# mod_tlars$get_R2()
# mod_tlars$get_RSS()
# mod_tlars$get_Cp()
# mod_tlars$get_lambda()
# mod_tlars$get_entry()
# mod_tlars$get_norm_X()
# mod_tlars$get_mean_X()
# mod_tlars$get_mean_y()
# mod_tlars$get_all()

---

Creates a Terminating-LARS (T-LARS) object

Description

Creates an object of the class tlars_cpp.

Usage

tlars_model(
  lars_state,
  X,
  y,
  num_dummies,
  verbose = FALSE,
  intercept = FALSE,
  standardize = TRUE,
  type = "lar",
  info = TRUE
)

Arguments

lars_state	List of variables associated with previous T-LARS step (necessary to restart the forward selection process exactly where it was previously terminated). The lars_state is extracted from an object of class tlars_cpp via get_all() and is only required when the object (or its pointer) of class tlars_cpp is deleted or got lost in another R session (e.g., in parallel processing).
X	Real valued predictor matrix.
y	Response vector.
num_dummies	Number of dummies that are appended to the predictor matrix.
verbose	Logical. If TRUE progress in computations is shown when performing T-LARS steps on the created model.
intercept	Logical. If TRUE an intercept is included.
standardize	Logical. If TRUE the predictors are standardized and the response is centered.
type	'lar' for 'LARS' and 'lasso' for Lasso.
info	Logical. If TRUE and object is not recreated from previous T-LARS state, then information about the created object is printed.

Value

Object of the class tlars_cpp.

Examples

data("Gauss_data")
X <- Gauss_data$X
y <- drop(Gauss_data$y)
p <- ncol(X)
n <- nrow(X)
num_dummies <- p
dummies <- matrix(stats::rnorm(n * p), nrow = n, ncol = num_dummies)
XD <- cbind(X, dummies)
mod_tlars <- tlars_model(X = XD, y = y, num_dummies = num_dummies)
mod_tlars

---