Package 'SplitReg'

Extract coefficients from a cv.SplitReg object.

Description

Extract coefficients from a cv.SplitReg object.

Usage

## S3 method for class 'cv.SplitReg'
coef(object, index = object$index_opt, ...)

Arguments

object	Fitted cv.SplitReg object.
index	Indices indicating values of lambda_S at which to extract coefficients. Defaults to the optimal value.
...	Additional arguments for compatibility.

Value

A vector of coefficients

See Also

cv.SplitReg

Examples

library(MASS)
set.seed(1)
beta <- c(rep(5, 5), rep(0, 45))
Sigma <- matrix(0.5, 50, 50)
diag(Sigma) <- 1
x <- mvrnorm(50, mu = rep(0, 50), Sigma = Sigma)
y <- x %*% beta + rnorm(50)
fit <- cv.SplitReg(x, y, num_models=2)
split.coefs <- coef(fit)

---

Split Regularized Regression algorithm with a sparsity and diversity penalty.

Description

Computes a split regularized regression estimator. The sparsity and diversity penalty parameters are chosen automatically.

Usage

cv.SplitReg(
  x,
  y,
  num_lambdas_sparsity = 100,
  num_lambdas_diversity = 100,
  alpha = 1,
  num_models = 10,
  tolerance = 1e-08,
  max_iter = 1e+05,
  num_folds = 10,
  num_threads = 1
)

Arguments

x	Design matrix.
y	Response vector.
num_lambdas_sparsity	Length of the grid of sparsity penalties.
num_lambdas_diversity	Length of the grid of diversity penalties.
alpha	Elastic Net tuning constant: the value must be between 0 and 1. Default is 1 (Lasso).
num_models	Number of models to build.
tolerance	Tolerance parameter to stop the iterations while cycling over the models.
max_iter	Maximum number of iterations before stopping the iterations while cycling over the models.
num_folds	Number of folds for cross-validating.
num_threads	Number of threads used for parallel computation over the folds.

Details

Computes a split regularized regression estimator with num_models ($G$) models, defined as the linear models $\boldsymbol{\beta}^{1},\dots, \boldsymbol{\beta}^{G}$ that minimize

$\sum\limits_{g=1}^{G}\left( \frac{1}{2n}\Vert \mathbf{y}-\mathbf{X} \boldsymbol{\beta}^{g}\Vert^{2} +\lambda_{S}\left( \frac{(1-\alpha)}{2}\Vert \boldsymbol{\beta}^{g}\Vert_{2}^{2}+\alpha \Vert \boldsymbol{ \beta \Vert_1}\right)+\frac{\lambda_{D}}{2}\sum\limits_{h\neq g}\sum_{j=1}^{p}\vert \beta_{j}^{h}\beta_{j}^{g}\vert \right),$

over grids for the penalty parameters $\lambda_{S}$ and $\lambda_{D}$ that are built automatically. Larger values of $\lambda_{S}$ encourage more sparsity within the models and larger values of $\lambda_{D}$ encourage more diversity among them. If $\lambda_{D}=0$, then all of the models are equal to the Elastic Net regularized least squares estimator with penalty parameter $\lambda_{S}$. Optimal penalty parameters are found by num_folds cross-validation, where the prediction of the ensemble is formed by simple averaging. The predictors and the response are standardized to zero mean and unit variance before any computations are performed. The final output is in the original scales.

Value

An object of class cv.SplitReg, a list with entries

betas	Coefficients computed over the path of penalties for sparsity; the penalty for diversity is fixed at the optimal value.
intercepts	Intercepts for each of the models along the path of penalties for sparsity.
index_opt	Index of the optimal penalty parameter for sparsity.
lambda_sparsity_opt	Optimal penalty parameter for sparsity.
lambda_diversity_opt	Optimal penalty parameter for diversity.
lambdas_sparsity	Grid of sparsity parameters.
lambdas_diversity	Grid of diversity parameters.
cv_mse_opt	Optimal CV MSE.
call	The matched call.

See Also

predict.cv.SplitReg, coef.cv.SplitReg

Examples

library(MASS)
set.seed(1)
beta <- c(rep(5, 5), rep(0, 45))
Sigma <- matrix(0.5, 50, 50)
diag(Sigma) <- 1
x <- mvrnorm(50, mu = rep(0, 50), Sigma = Sigma)
y <- x %*% beta + rnorm(50)
fit <- cv.SplitReg(x, y, num_models=2)
coefs <- predict(fit, type="coefficients")

---

Make predictions from a cv.SplitReg object.

Description

Make predictions from a cv.SplitReg object, similar to other predict methods.

Usage

## S3 method for class 'cv.SplitReg'
predict(
  object,
  newx,
  index = object$index_opt,
  type = c("response", "coefficients"),
  ...
)

Arguments

object	Fitted cv.SplitReg object.
newx	Matrix of new values of x at which prediction are to be made. Ignored if type is "coefficients".
index	Indices indicating values of lambda_S at which to predict. Defaults to the optimal value.
type	Either "response" for predicted values or "coefficients" for the estimated coefficients.
...	Additional arguments for compatibility.

Value

Either a matrix with predictions or a vector of coefficients

See Also

predict.cv.SplitReg

Examples

library(MASS)
set.seed(1)
beta <- c(rep(5, 5), rep(0, 45))
Sigma <- matrix(0.5, 50, 50)
diag(Sigma) <- 1
x <- mvrnorm(50, mu = rep(0, 50), Sigma = Sigma)
y <- x %*% beta + rnorm(50)
fit <- cv.SplitReg(x, y, num_models=2)
x.new <- mvrnorm(50, mu = rep(0, 50), Sigma = Sigma)
split.predictions <- predict(fit, newx = x.new, type="response")

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