| Title: | Stepwise Split Regularized Regression |
|---|---|
| Description: | Functions to perform stepwise split regularized regression. The approach first uses a stepwise algorithm to split the variables into the models with a goodness of fit criterion, and then regularization is applied to each model. The weights of the models in the ensemble are determined based on a criterion selected by the user. |
| Authors: | Anthony Christidis [aut, cre], Stefan Van Aelst [aut], Ruben Zamar [aut] |
| Maintainer: | Anthony Christidis <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0.3 |
| Built: | 2024-11-02 06:34:04 UTC |
| Source: | CRAN |
coef.cv.stepSplitReg returns the coefficients for a cv.stepSplitReg object.
## S3 method for class 'cv.stepSplitReg' coef(object, group_index = NULL, ...)## S3 method for class 'cv.stepSplitReg' coef(object, group_index = NULL, ...)
object |
An object of class cv.stepSplitReg |
group_index |
Groups included in the ensemble. Default setting includes all the groups. |
... |
Additional arguments for compatibility. |
The coefficients for the cv.stepSplitReg object.
Anthony-Alexander Christidis, [email protected]
# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 30 n.test <- 500 sparsity <- 0.2 rho <- 0.5 SNR <- 3 # Generating the coefficient p.active <- floor(p*sparsity) a <- 4*log(n)/sqrt(n) neg.prob <- 0.2 nonzero.betas <- (-1)^(rbinom(p.active, 1, neg.prob))*(a + abs(rnorm(p.active))) # Correlation structure Sigma <- matrix(0, p, p) Sigma[1:p.active, 1:p.active] <- rho diag(Sigma) <- 1 true.beta <- c(nonzero.betas, rep(0 , p - p.active)) # Computing the noise parameter for target SNR sigma.epsilon <- as.numeric(sqrt((t(true.beta) %*% Sigma %*% true.beta)/SNR)) # Simulate some data set.seed(1) x.train <- mvnfast::rmvn(n, mu=rep(0,p), sigma=Sigma) y.train <- 1 + x.train %*% true.beta + rnorm(n=n, mean=0, sd=sigma.epsilon) x.test <- mvnfast::rmvn(n.test, mu=rep(0,p), sigma=Sigma) y.test <- 1 + x.test %*% true.beta + rnorm(n.test, sd=sigma.epsilon) # Stepwise Split Regularized Regression step.out <- cv.stepSplitReg(x.train, y.train, n_models = c(2, 3), max_variables = NULL, keep = 4/4, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 4/4, include_intercept = TRUE, n_lambda = 50, tolerance = 1e-2, max_iter = 1e5, n_folds = 5, model_weights = c("Equal", "Proportional", "Stacking")[1], n_threads = 1) step.coefficients <- coef(step.out, group_index = 1:step.out$n_models_optimal) step.predictions <- predict(step.out, x.test, group_index = 1:step.out$n_models_optimal) mspe.step <- mean((step.predictions-y.test)^2)/sigma.epsilon^2# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 30 n.test <- 500 sparsity <- 0.2 rho <- 0.5 SNR <- 3 # Generating the coefficient p.active <- floor(p*sparsity) a <- 4*log(n)/sqrt(n) neg.prob <- 0.2 nonzero.betas <- (-1)^(rbinom(p.active, 1, neg.prob))*(a + abs(rnorm(p.active))) # Correlation structure Sigma <- matrix(0, p, p) Sigma[1:p.active, 1:p.active] <- rho diag(Sigma) <- 1 true.beta <- c(nonzero.betas, rep(0 , p - p.active)) # Computing the noise parameter for target SNR sigma.epsilon <- as.numeric(sqrt((t(true.beta) %*% Sigma %*% true.beta)/SNR)) # Simulate some data set.seed(1) x.train <- mvnfast::rmvn(n, mu=rep(0,p), sigma=Sigma) y.train <- 1 + x.train %*% true.beta + rnorm(n=n, mean=0, sd=sigma.epsilon) x.test <- mvnfast::rmvn(n.test, mu=rep(0,p), sigma=Sigma) y.test <- 1 + x.test %*% true.beta + rnorm(n.test, sd=sigma.epsilon) # Stepwise Split Regularized Regression step.out <- cv.stepSplitReg(x.train, y.train, n_models = c(2, 3), max_variables = NULL, keep = 4/4, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 4/4, include_intercept = TRUE, n_lambda = 50, tolerance = 1e-2, max_iter = 1e5, n_folds = 5, model_weights = c("Equal", "Proportional", "Stacking")[1], n_threads = 1) step.coefficients <- coef(step.out, group_index = 1:step.out$n_models_optimal) step.predictions <- predict(step.out, x.test, group_index = 1:step.out$n_models_optimal) mspe.step <- mean((step.predictions-y.test)^2)/sigma.epsilon^2
coef.stepSplitReg returns the coefficients for a stepSplitReg object.
## S3 method for class 'stepSplitReg' coef(object, group_index = NULL, ...)## S3 method for class 'stepSplitReg' coef(object, group_index = NULL, ...)
object |
An object of class stepSplitReg |
group_index |
Groups included in the ensemble. Default setting includes all the groups. |
... |
Additional arguments for compatibility. |
The coefficients for the stepSplitReg object.
Anthony-Alexander Christidis, [email protected]
# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 30 n.test <- 1000 sparsity <- 0.2 rho <- 0.5 SNR <- 3 # Generating the coefficient p.active <- floor(p*sparsity) a <- 4*log(n)/sqrt(n) neg.prob <- 0.2 nonzero.betas <- (-1)^(rbinom(p.active, 1, neg.prob))*(a + abs(rnorm(p.active))) # Correlation structure Sigma <- matrix(0, p, p) Sigma[1:p.active, 1:p.active] <- rho diag(Sigma) <- 1 true.beta <- c(nonzero.betas, rep(0 , p - p.active)) # Computing the noise parameter for target SNR sigma.epsilon <- as.numeric(sqrt((t(true.beta) %*% Sigma %*% true.beta)/SNR)) # Simulate some data set.seed(1) x.train <- mvnfast::rmvn(n, mu=rep(0,p), sigma=Sigma) y.train <- 1 + x.train %*% true.beta + rnorm(n=n, mean=0, sd=sigma.epsilon) x.test <- mvnfast::rmvn(n.test, mu=rep(0,p), sigma=Sigma) y.test <- 1 + x.test %*% true.beta + rnorm(n.test, sd=sigma.epsilon) # Stepwise Split Regularized Regression step.out <- stepSplitReg(x.train, y.train, n_models = 3, max_variables = NULL, keep = 4/4, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 4/4, include_intercept = TRUE, n_lambda = 50, tolerance = 1e-2, max_iter = 1e5, n_folds = 5, model_weights = c("Equal", "Proportional", "Stacking")[1]) step.coefficients <- coef(step.out, group_index = 1:step.out$n_models) step.predictions <- predict(step.out, x.test, group_index = 1:step.out$n_models) mspe.step <- mean((step.predictions-y.test)^2)/sigma.epsilon^2# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 30 n.test <- 1000 sparsity <- 0.2 rho <- 0.5 SNR <- 3 # Generating the coefficient p.active <- floor(p*sparsity) a <- 4*log(n)/sqrt(n) neg.prob <- 0.2 nonzero.betas <- (-1)^(rbinom(p.active, 1, neg.prob))*(a + abs(rnorm(p.active))) # Correlation structure Sigma <- matrix(0, p, p) Sigma[1:p.active, 1:p.active] <- rho diag(Sigma) <- 1 true.beta <- c(nonzero.betas, rep(0 , p - p.active)) # Computing the noise parameter for target SNR sigma.epsilon <- as.numeric(sqrt((t(true.beta) %*% Sigma %*% true.beta)/SNR)) # Simulate some data set.seed(1) x.train <- mvnfast::rmvn(n, mu=rep(0,p), sigma=Sigma) y.train <- 1 + x.train %*% true.beta + rnorm(n=n, mean=0, sd=sigma.epsilon) x.test <- mvnfast::rmvn(n.test, mu=rep(0,p), sigma=Sigma) y.test <- 1 + x.test %*% true.beta + rnorm(n.test, sd=sigma.epsilon) # Stepwise Split Regularized Regression step.out <- stepSplitReg(x.train, y.train, n_models = 3, max_variables = NULL, keep = 4/4, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 4/4, include_intercept = TRUE, n_lambda = 50, tolerance = 1e-2, max_iter = 1e5, n_folds = 5, model_weights = c("Equal", "Proportional", "Stacking")[1]) step.coefficients <- coef(step.out, group_index = 1:step.out$n_models) step.predictions <- predict(step.out, x.test, group_index = 1:step.out$n_models) mspe.step <- mean((step.predictions-y.test)^2)/sigma.epsilon^2
cv.stepSplitReg performs the CV procedure for stepwise split regularized regression.
cv.stepSplitReg( x, y, n_models = NULL, max_variables = NULL, keep = 1, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 3/4, include_intercept = TRUE, n_lambda = 100, tolerance = 0.001, max_iter = 1e+05, n_folds = 10, model_weights = c("Equal", "Proportional", "Stacking")[1], n_threads = 1 )cv.stepSplitReg( x, y, n_models = NULL, max_variables = NULL, keep = 1, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 3/4, include_intercept = TRUE, n_lambda = 100, tolerance = 0.001, max_iter = 1e+05, n_folds = 10, model_weights = c("Equal", "Proportional", "Stacking")[1], n_threads = 1 )
x |
Design matrix. |
y |
Response vector. |
n_models |
Number of models into which the variables are split. |
max_variables |
Maximum number of variables that a model can contain. |
keep |
Proportion of models to keep based on their individual cross-validated errors. Default is 1. |
model_criterion |
Criterion for adding a variable to a model. Must be one of c("F-test", "RSS"). Default is "F-test". |
stop_criterion |
Criterion for determining when a model is saturated. Must be one of c("F-test", "pR2", "aR2", "R2", "Fixed"). Default is "F-test". |
stop_parameter |
Parameter value for the stopping criterion. Default is 0.05 for "F-test". |
shrinkage |
TRUE or FALSE parameter for shrinkage of the final models. Default is TRUE. |
alpha |
Elastic net mixing parmeter for model shrinkage. Default is 3/4. |
include_intercept |
TRUE or FALSE parameter for the inclusion of an intercept term. |
n_lambda |
Number of candidates for the sparsity penalty parameter. Default is 100. |
tolerance |
Convergence criteria for the coefficients. Default is 1e-3. |
max_iter |
Maximum number of iterations in the algorithm. Default is 1e5. |
n_folds |
Number of cross-validation folds. Default is 10. |
model_weights |
Criterion to determine the weights of the model for prediciton. Must be one of c("Equal", "Proportional", "Stacking"). Default is "Equal". |
n_threads |
Number of threads. Default is 1. |
An object of class cv.stepSplitReg.
Anthony-Alexander Christidis, [email protected]
coef.cv.stepSplitReg, predict.cv.stepSplitReg
# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 30 n.test <- 500 sparsity <- 0.2 rho <- 0.5 SNR <- 3 # Generating the coefficient p.active <- floor(p*sparsity) a <- 4*log(n)/sqrt(n) neg.prob <- 0.2 nonzero.betas <- (-1)^(rbinom(p.active, 1, neg.prob))*(a + abs(rnorm(p.active))) # Correlation structure Sigma <- matrix(0, p, p) Sigma[1:p.active, 1:p.active] <- rho diag(Sigma) <- 1 true.beta <- c(nonzero.betas, rep(0 , p - p.active)) # Computing the noise parameter for target SNR sigma.epsilon <- as.numeric(sqrt((t(true.beta) %*% Sigma %*% true.beta)/SNR)) # Simulate some data set.seed(1) x.train <- mvnfast::rmvn(n, mu=rep(0,p), sigma=Sigma) y.train <- 1 + x.train %*% true.beta + rnorm(n=n, mean=0, sd=sigma.epsilon) x.test <- mvnfast::rmvn(n.test, mu=rep(0,p), sigma=Sigma) y.test <- 1 + x.test %*% true.beta + rnorm(n.test, sd=sigma.epsilon) # Stepwise Split Regularized Regression step.out <- cv.stepSplitReg(x.train, y.train, n_models = c(2, 3), max_variables = NULL, keep = 4/4, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 4/4, include_intercept = TRUE, n_lambda = 50, tolerance = 1e-2, max_iter = 1e5, n_folds = 5, model_weights = c("Equal", "Proportional", "Stacking")[1], n_threads = 1) step.coefficients <- coef(step.out, group_index = 1:step.out$n_models_optimal) step.predictions <- predict(step.out, x.test, group_index = 1:step.out$n_models_optimal) mspe.step <- mean((step.predictions-y.test)^2)/sigma.epsilon^2# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 30 n.test <- 500 sparsity <- 0.2 rho <- 0.5 SNR <- 3 # Generating the coefficient p.active <- floor(p*sparsity) a <- 4*log(n)/sqrt(n) neg.prob <- 0.2 nonzero.betas <- (-1)^(rbinom(p.active, 1, neg.prob))*(a + abs(rnorm(p.active))) # Correlation structure Sigma <- matrix(0, p, p) Sigma[1:p.active, 1:p.active] <- rho diag(Sigma) <- 1 true.beta <- c(nonzero.betas, rep(0 , p - p.active)) # Computing the noise parameter for target SNR sigma.epsilon <- as.numeric(sqrt((t(true.beta) %*% Sigma %*% true.beta)/SNR)) # Simulate some data set.seed(1) x.train <- mvnfast::rmvn(n, mu=rep(0,p), sigma=Sigma) y.train <- 1 + x.train %*% true.beta + rnorm(n=n, mean=0, sd=sigma.epsilon) x.test <- mvnfast::rmvn(n.test, mu=rep(0,p), sigma=Sigma) y.test <- 1 + x.test %*% true.beta + rnorm(n.test, sd=sigma.epsilon) # Stepwise Split Regularized Regression step.out <- cv.stepSplitReg(x.train, y.train, n_models = c(2, 3), max_variables = NULL, keep = 4/4, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 4/4, include_intercept = TRUE, n_lambda = 50, tolerance = 1e-2, max_iter = 1e5, n_folds = 5, model_weights = c("Equal", "Proportional", "Stacking")[1], n_threads = 1) step.coefficients <- coef(step.out, group_index = 1:step.out$n_models_optimal) step.predictions <- predict(step.out, x.test, group_index = 1:step.out$n_models_optimal) mspe.step <- mean((step.predictions-y.test)^2)/sigma.epsilon^2
predict.cv.stepSplitReg returns the predictions for a cv.stepSplitReg object.
## S3 method for class 'cv.stepSplitReg' predict(object, newx, group_index = group_index, ...)## S3 method for class 'cv.stepSplitReg' predict(object, newx, group_index = group_index, ...)
object |
An object of class cv.stepSplitReg |
newx |
New data for predictions. |
group_index |
Groups included in the ensemble. Default setting includes all the groups. |
... |
Additional arguments for compatibility. |
The predictions for the cv.stepSplitReg object.
Anthony-Alexander Christidis, [email protected]
# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 30 n.test <- 500 sparsity <- 0.2 rho <- 0.5 SNR <- 3 # Generating the coefficient p.active <- floor(p*sparsity) a <- 4*log(n)/sqrt(n) neg.prob <- 0.2 nonzero.betas <- (-1)^(rbinom(p.active, 1, neg.prob))*(a + abs(rnorm(p.active))) # Correlation structure Sigma <- matrix(0, p, p) Sigma[1:p.active, 1:p.active] <- rho diag(Sigma) <- 1 true.beta <- c(nonzero.betas, rep(0 , p - p.active)) # Computing the noise parameter for target SNR sigma.epsilon <- as.numeric(sqrt((t(true.beta) %*% Sigma %*% true.beta)/SNR)) # Simulate some data set.seed(1) x.train <- mvnfast::rmvn(n, mu=rep(0,p), sigma=Sigma) y.train <- 1 + x.train %*% true.beta + rnorm(n=n, mean=0, sd=sigma.epsilon) x.test <- mvnfast::rmvn(n.test, mu=rep(0,p), sigma=Sigma) y.test <- 1 + x.test %*% true.beta + rnorm(n.test, sd=sigma.epsilon) # Stepwise Split Regularized Regression step.out <- cv.stepSplitReg(x.train, y.train, n_models = c(2, 3), max_variables = NULL, keep = 4/4, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 4/4, include_intercept = TRUE, n_lambda = 50, tolerance = 1e-2, max_iter = 1e5, n_folds = 5, model_weights = c("Equal", "Proportional", "Stacking")[1], n_threads = 1) step.coefficients <- coef(step.out, group_index = 1:step.out$n_models_optimal) step.predictions <- predict(step.out, x.test, group_index = 1:step.out$n_models_optimal) mspe.step <- mean((step.predictions-y.test)^2)/sigma.epsilon^2# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 30 n.test <- 500 sparsity <- 0.2 rho <- 0.5 SNR <- 3 # Generating the coefficient p.active <- floor(p*sparsity) a <- 4*log(n)/sqrt(n) neg.prob <- 0.2 nonzero.betas <- (-1)^(rbinom(p.active, 1, neg.prob))*(a + abs(rnorm(p.active))) # Correlation structure Sigma <- matrix(0, p, p) Sigma[1:p.active, 1:p.active] <- rho diag(Sigma) <- 1 true.beta <- c(nonzero.betas, rep(0 , p - p.active)) # Computing the noise parameter for target SNR sigma.epsilon <- as.numeric(sqrt((t(true.beta) %*% Sigma %*% true.beta)/SNR)) # Simulate some data set.seed(1) x.train <- mvnfast::rmvn(n, mu=rep(0,p), sigma=Sigma) y.train <- 1 + x.train %*% true.beta + rnorm(n=n, mean=0, sd=sigma.epsilon) x.test <- mvnfast::rmvn(n.test, mu=rep(0,p), sigma=Sigma) y.test <- 1 + x.test %*% true.beta + rnorm(n.test, sd=sigma.epsilon) # Stepwise Split Regularized Regression step.out <- cv.stepSplitReg(x.train, y.train, n_models = c(2, 3), max_variables = NULL, keep = 4/4, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 4/4, include_intercept = TRUE, n_lambda = 50, tolerance = 1e-2, max_iter = 1e5, n_folds = 5, model_weights = c("Equal", "Proportional", "Stacking")[1], n_threads = 1) step.coefficients <- coef(step.out, group_index = 1:step.out$n_models_optimal) step.predictions <- predict(step.out, x.test, group_index = 1:step.out$n_models_optimal) mspe.step <- mean((step.predictions-y.test)^2)/sigma.epsilon^2
predict.stepSplitReg returns the predictions for a stepSplitReg object.
## S3 method for class 'stepSplitReg' predict(object, newx, group_index = NULL, ...)## S3 method for class 'stepSplitReg' predict(object, newx, group_index = NULL, ...)
object |
An object of class stepSplitReg |
newx |
New data for predictions. |
group_index |
Groups included in the ensemble. Default setting includes all the groups. |
... |
Additional arguments for compatibility. |
The predictions for the stepSplitReg object.
Anthony-Alexander Christidis, [email protected]
# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 30 n.test <- 1000 sparsity <- 0.2 rho <- 0.5 SNR <- 3 # Generating the coefficient p.active <- floor(p*sparsity) a <- 4*log(n)/sqrt(n) neg.prob <- 0.2 nonzero.betas <- (-1)^(rbinom(p.active, 1, neg.prob))*(a + abs(rnorm(p.active))) # Correlation structure Sigma <- matrix(0, p, p) Sigma[1:p.active, 1:p.active] <- rho diag(Sigma) <- 1 true.beta <- c(nonzero.betas, rep(0 , p - p.active)) # Computing the noise parameter for target SNR sigma.epsilon <- as.numeric(sqrt((t(true.beta) %*% Sigma %*% true.beta)/SNR)) # Simulate some data set.seed(1) x.train <- mvnfast::rmvn(n, mu=rep(0,p), sigma=Sigma) y.train <- 1 + x.train %*% true.beta + rnorm(n=n, mean=0, sd=sigma.epsilon) x.test <- mvnfast::rmvn(n.test, mu=rep(0,p), sigma=Sigma) y.test <- 1 + x.test %*% true.beta + rnorm(n.test, sd=sigma.epsilon) # Stepwise Split Regularized Regression step.out <- stepSplitReg(x.train, y.train, n_models = 3, max_variables = NULL, keep = 4/4, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 4/4, include_intercept = TRUE, n_lambda = 50, tolerance = 1e-2, max_iter = 1e5, n_folds = 5, model_weights = c("Equal", "Proportional", "Stacking")[1]) step.coefficients <- coef(step.out, group_index = 1:step.out$n_models) step.predictions <- predict(step.out, x.test, group_index = 1:step.out$n_models) mspe.step <- mean((step.predictions-y.test)^2)/sigma.epsilon^2# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 30 n.test <- 1000 sparsity <- 0.2 rho <- 0.5 SNR <- 3 # Generating the coefficient p.active <- floor(p*sparsity) a <- 4*log(n)/sqrt(n) neg.prob <- 0.2 nonzero.betas <- (-1)^(rbinom(p.active, 1, neg.prob))*(a + abs(rnorm(p.active))) # Correlation structure Sigma <- matrix(0, p, p) Sigma[1:p.active, 1:p.active] <- rho diag(Sigma) <- 1 true.beta <- c(nonzero.betas, rep(0 , p - p.active)) # Computing the noise parameter for target SNR sigma.epsilon <- as.numeric(sqrt((t(true.beta) %*% Sigma %*% true.beta)/SNR)) # Simulate some data set.seed(1) x.train <- mvnfast::rmvn(n, mu=rep(0,p), sigma=Sigma) y.train <- 1 + x.train %*% true.beta + rnorm(n=n, mean=0, sd=sigma.epsilon) x.test <- mvnfast::rmvn(n.test, mu=rep(0,p), sigma=Sigma) y.test <- 1 + x.test %*% true.beta + rnorm(n.test, sd=sigma.epsilon) # Stepwise Split Regularized Regression step.out <- stepSplitReg(x.train, y.train, n_models = 3, max_variables = NULL, keep = 4/4, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 4/4, include_intercept = TRUE, n_lambda = 50, tolerance = 1e-2, max_iter = 1e5, n_folds = 5, model_weights = c("Equal", "Proportional", "Stacking")[1]) step.coefficients <- coef(step.out, group_index = 1:step.out$n_models) step.predictions <- predict(step.out, x.test, group_index = 1:step.out$n_models) mspe.step <- mean((step.predictions-y.test)^2)/sigma.epsilon^2
stepSplitReg performs stepwise split regularized regression.
stepSplitReg( x, y, n_models = NULL, max_variables = NULL, keep = 1, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 3/4, include_intercept = TRUE, n_lambda = 100, tolerance = 0.001, max_iter = 1e+05, n_folds = 10, model_weights = c("Equal", "Proportional", "Stacking")[1] )stepSplitReg( x, y, n_models = NULL, max_variables = NULL, keep = 1, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 3/4, include_intercept = TRUE, n_lambda = 100, tolerance = 0.001, max_iter = 1e+05, n_folds = 10, model_weights = c("Equal", "Proportional", "Stacking")[1] )
x |
Design matrix. |
y |
Response vector. |
n_models |
Number of models into which the variables are split. |
max_variables |
Maximum number of variables that a model can contain. |
keep |
Proportion of models to keep based on their individual cross-validated errors. Default is 1. |
model_criterion |
Criterion for adding a variable to a model. Must be one of c("F-test", "RSS"). Default is "F-test". |
stop_criterion |
Criterion for determining when a model is saturated. Must be one of c("F-test", "pR2", "aR2", "R2", "Fixed"). Default is "F-test". |
stop_parameter |
Parameter value for the stopping criterion. Default is 0.05 for "F-test". |
shrinkage |
TRUE or FALSE parameter for shrinkage of the final models. Default is TRUE. |
alpha |
Elastic net mixing parmeter for model shrinkage. Default is 3/4. |
include_intercept |
TRUE or FALSE parameter for the inclusion of an intercept term. |
n_lambda |
Number of candidates for the sparsity penalty parameter. Default is 100. |
tolerance |
Convergence criteria for the coefficients. Default is 1e-3. |
max_iter |
Maximum number of iterations in the algorithm. Default is 1e5. |
n_folds |
Number of cross-validation folds. Default is 10. |
model_weights |
Criterion to determine the weights of the model for prediciton. Must be one of c("Equal", "Proportional", "Stacking"). Default is "Equal". |
An object of class stepSplitReg.
Anthony-Alexander Christidis, [email protected]
coef.stepSplitReg, predict.stepSplitReg
# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 30 n.test <- 1000 sparsity <- 0.2 rho <- 0.5 SNR <- 3 # Generating the coefficient p.active <- floor(p*sparsity) a <- 4*log(n)/sqrt(n) neg.prob <- 0.2 nonzero.betas <- (-1)^(rbinom(p.active, 1, neg.prob))*(a + abs(rnorm(p.active))) # Correlation structure Sigma <- matrix(0, p, p) Sigma[1:p.active, 1:p.active] <- rho diag(Sigma) <- 1 true.beta <- c(nonzero.betas, rep(0 , p - p.active)) # Computing the noise parameter for target SNR sigma.epsilon <- as.numeric(sqrt((t(true.beta) %*% Sigma %*% true.beta)/SNR)) # Simulate some data set.seed(1) x.train <- mvnfast::rmvn(n, mu=rep(0,p), sigma=Sigma) y.train <- 1 + x.train %*% true.beta + rnorm(n=n, mean=0, sd=sigma.epsilon) x.test <- mvnfast::rmvn(n.test, mu=rep(0,p), sigma=Sigma) y.test <- 1 + x.test %*% true.beta + rnorm(n.test, sd=sigma.epsilon) # Stepwise Split Regularized Regression step.out <- stepSplitReg(x.train, y.train, n_models = 3, max_variables = NULL, keep = 4/4, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 4/4, include_intercept = TRUE, n_lambda = 50, tolerance = 1e-2, max_iter = 1e5, n_folds = 5, model_weights = c("Equal", "Proportional", "Stacking")[1]) step.coefficients <- coef(step.out, group_index = 1:step.out$n_models) step.predictions <- predict(step.out, x.test, group_index = 1:step.out$n_models) mspe.step <- mean((step.predictions-y.test)^2)/sigma.epsilon^2# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 30 n.test <- 1000 sparsity <- 0.2 rho <- 0.5 SNR <- 3 # Generating the coefficient p.active <- floor(p*sparsity) a <- 4*log(n)/sqrt(n) neg.prob <- 0.2 nonzero.betas <- (-1)^(rbinom(p.active, 1, neg.prob))*(a + abs(rnorm(p.active))) # Correlation structure Sigma <- matrix(0, p, p) Sigma[1:p.active, 1:p.active] <- rho diag(Sigma) <- 1 true.beta <- c(nonzero.betas, rep(0 , p - p.active)) # Computing the noise parameter for target SNR sigma.epsilon <- as.numeric(sqrt((t(true.beta) %*% Sigma %*% true.beta)/SNR)) # Simulate some data set.seed(1) x.train <- mvnfast::rmvn(n, mu=rep(0,p), sigma=Sigma) y.train <- 1 + x.train %*% true.beta + rnorm(n=n, mean=0, sd=sigma.epsilon) x.test <- mvnfast::rmvn(n.test, mu=rep(0,p), sigma=Sigma) y.test <- 1 + x.test %*% true.beta + rnorm(n.test, sd=sigma.epsilon) # Stepwise Split Regularized Regression step.out <- stepSplitReg(x.train, y.train, n_models = 3, max_variables = NULL, keep = 4/4, model_criterion = c("F-test", "RSS")[1], stop_criterion = c("F-test", "pR2", "aR2", "R2", "Fixed")[1], stop_parameter = 0.05, shrinkage = TRUE, alpha = 4/4, include_intercept = TRUE, n_lambda = 50, tolerance = 1e-2, max_iter = 1e5, n_folds = 5, model_weights = c("Equal", "Proportional", "Stacking")[1]) step.coefficients <- coef(step.out, group_index = 1:step.out$n_models) step.predictions <- predict(step.out, x.test, group_index = 1:step.out$n_models) mspe.step <- mean((step.predictions-y.test)^2)/sigma.epsilon^2