| Title: | Projected Subset Gradient Descent |
|---|---|
| Description: | Functions to generate ensembles of generalized linear models using a greedy projected subset gradient descent algorithm. The sparsity and diversity tuning parameters are selected by cross-validation. |
| 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: | 2024-11-01 05:25:17 UTC |
| Source: | https://github.com/anthonychristidis/psgd |
coef.cv.PSGD returns the coefficients for a cv.PSGD object.
## S3 method for class 'cv.PSGD' coef(object, group_index = NULL, ...)## S3 method for class 'cv.PSGD' coef(object, group_index = NULL, ...)
object |
An object of class cv.PSGD |
group_index |
Groups included in the ensemble. Default setting includes all the groups. |
... |
Additional arguments for compatibility. |
The coefficients for the cv.PSGD object.
Anthony-Alexander Christidis, [email protected]
# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 40 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) # CV PSGD Ensemble output <- cv.PSGD(x = x.train, y = y.train, n_models = 5, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split_grid = c(2, 3), size_grid = c(10, 15), max_iter = 20, cycling_iter = 0, n_folds = 5, n_threads = 1) psgd.coef <- coef(output, group_index = 1:output$n_models) psgd.predictions <- predict(output, newx = x.test, group_index = 1:output$n_models) mean((y.test - psgd.predictions)^2)/sigma.epsilon^2# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 40 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) # CV PSGD Ensemble output <- cv.PSGD(x = x.train, y = y.train, n_models = 5, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split_grid = c(2, 3), size_grid = c(10, 15), max_iter = 20, cycling_iter = 0, n_folds = 5, n_threads = 1) psgd.coef <- coef(output, group_index = 1:output$n_models) psgd.predictions <- predict(output, newx = x.test, group_index = 1:output$n_models) mean((y.test - psgd.predictions)^2)/sigma.epsilon^2
coef.PSGD returns the coefficients for a PSGD object.
## S3 method for class 'PSGD' coef(object, group_index = NULL, ...)## S3 method for class 'PSGD' coef(object, group_index = NULL, ...)
object |
An object of class PSGD. |
group_index |
Groups included in the ensemble. Default setting includes all the groups. |
... |
Additional arguments for compatibility. |
The coefficients for the PSGD object.
Anthony-Alexander Christidis, [email protected]
# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 40 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) # PSGD Ensemble output <- PSGD(x = x.train, y = y.train, n_models = 5, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split = 3, size = 10, max_iter = 20, cycling_iter = 0) psgd.coef <- coef(output, group_index = 1:output$n_models) psgd.predictions <- predict(output, newx = x.test, group_index = 1:output$n_models) mean((y.test - psgd.predictions)^2)/sigma.epsilon^2# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 40 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) # PSGD Ensemble output <- PSGD(x = x.train, y = y.train, n_models = 5, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split = 3, size = 10, max_iter = 20, cycling_iter = 0) psgd.coef <- coef(output, group_index = 1:output$n_models) psgd.predictions <- predict(output, newx = x.test, group_index = 1:output$n_models) mean((y.test - psgd.predictions)^2)/sigma.epsilon^2
cv.PSGD performs the CV procedure for a projected subset gradient descent algorithm.
cv.PSGD( x, y, n_models, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split_grid, size_grid, max_iter = 100, cycling_iter = 5, n_folds = 5, n_threads = 1 )cv.PSGD( x, y, n_models, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split_grid, size_grid, max_iter = 100, cycling_iter = 5, n_folds = 5, n_threads = 1 )
x |
Design matrix. |
y |
Response vector. |
n_models |
Number of models into which the variables are split. |
model_type |
Model type. Must be one of "Linear or Logistic". Default is "Linear". |
include_intercept |
TRUE or FALSE parameter for the inclusion of an intercept term. Default is TRUE. |
split_grid |
Grid for number of models that may share a variable. |
size_grid |
Grid for number of variables that a model may have. |
max_iter |
Maximum number of iterations in PSGD algorithm. |
cycling_iter |
Number of random cycling permutations. |
n_folds |
Number of cross-validation folds. Default is 5 |
n_threads |
Number of threads. Default is 1. |
An object of class cv.PSGD
Anthony-Alexander Christidis, [email protected]
# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 40 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) # CV PSGD Ensemble output <- cv.PSGD(x = x.train, y = y.train, n_models = 5, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split_grid = c(2, 3), size_grid = c(10, 15), max_iter = 20, cycling_iter = 0, n_folds = 5, n_threads = 1) psgd.coef <- coef(output, group_index = 1:output$n_models) psgd.predictions <- predict(output, newx = x.test, group_index = 1:output$n_models) mean((y.test - psgd.predictions)^2)/sigma.epsilon^2# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 40 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) # CV PSGD Ensemble output <- cv.PSGD(x = x.train, y = y.train, n_models = 5, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split_grid = c(2, 3), size_grid = c(10, 15), max_iter = 20, cycling_iter = 0, n_folds = 5, n_threads = 1) psgd.coef <- coef(output, group_index = 1:output$n_models) psgd.predictions <- predict(output, newx = x.test, group_index = 1:output$n_models) mean((y.test - psgd.predictions)^2)/sigma.epsilon^2
predict.cv.PSGD returns the predictions for a cv.PSGD object.
## S3 method for class 'cv.PSGD' predict(object, newx, group_index = group_index, ...)## S3 method for class 'cv.PSGD' predict(object, newx, group_index = group_index, ...)
object |
An object of class cv.PSGD |
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.PSGD object.
Anthony-Alexander Christidis, [email protected]
# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 40 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) # CV PSGD Ensemble output <- cv.PSGD(x = x.train, y = y.train, n_models = 5, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split_grid = c(2, 3), size_grid = c(10, 15), max_iter = 20, cycling_iter = 0, n_folds = 5, n_threads = 1) psgd.coef <- coef(output, group_index = 1:output$n_models) psgd.predictions <- predict(output, newx = x.test, group_index = 1:output$n_models) mean((y.test - psgd.predictions)^2)/sigma.epsilon^2# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 40 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) # CV PSGD Ensemble output <- cv.PSGD(x = x.train, y = y.train, n_models = 5, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split_grid = c(2, 3), size_grid = c(10, 15), max_iter = 20, cycling_iter = 0, n_folds = 5, n_threads = 1) psgd.coef <- coef(output, group_index = 1:output$n_models) psgd.predictions <- predict(output, newx = x.test, group_index = 1:output$n_models) mean((y.test - psgd.predictions)^2)/sigma.epsilon^2
predict.PSGD returns the predictions for a PSGD object.
## S3 method for class 'PSGD' predict(object, newx, group_index = NULL, ...)## S3 method for class 'PSGD' predict(object, newx, group_index = NULL, ...)
object |
An object of class PSGD |
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 PSGD object.
Anthony-Alexander Christidis, [email protected]
# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 40 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) # PSGD Ensemble output <- PSGD(x = x.train, y = y.train, n_models = 5, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split = 3, size = 10, max_iter = 20, cycling_iter = 0) psgd.coef <- coef(output, group_index = 1:output$n_models) psgd.predictions <- predict(output, newx = x.test, group_index = 1:output$n_models) mean((y.test - psgd.predictions)^2)/sigma.epsilon^2# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 40 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) # PSGD Ensemble output <- PSGD(x = x.train, y = y.train, n_models = 5, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split = 3, size = 10, max_iter = 20, cycling_iter = 0) psgd.coef <- coef(output, group_index = 1:output$n_models) psgd.predictions <- predict(output, newx = x.test, group_index = 1:output$n_models) mean((y.test - psgd.predictions)^2)/sigma.epsilon^2
PSGD performs a projected subset gradient descent algorithm.
PSGD( x, y, n_models, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split, size, max_iter = 100, cycling_iter = 5 )PSGD( x, y, n_models, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split, size, max_iter = 100, cycling_iter = 5 )
x |
Design matrix. |
y |
Response vector. |
n_models |
Number of models into which the variables are split. |
model_type |
Model type. Must be one of "Linear or Logistic". Default is "Linear". |
include_intercept |
TRUE or FALSE parameter for the inclusion of an intercept term. Default is TRUE. |
split |
Number of models that may share a variable. |
size |
Number of variables that a model may have. |
max_iter |
Maximum number of iterations in PSGD algorithm. |
cycling_iter |
Number of random cycling permutations. |
An object of class PSGD
Anthony-Alexander Christidis, [email protected]
# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 40 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) # PSGD Ensemble output <- PSGD(x = x.train, y = y.train, n_models = 5, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split = 3, size = 10, max_iter = 20, cycling_iter = 0) psgd.coef <- coef(output, group_index = 1:output$n_models) psgd.predictions <- predict(output, newx = x.test, group_index = 1:output$n_models) mean((y.test - psgd.predictions)^2)/sigma.epsilon^2# Required Libraries library(mvnfast) # Setting the parameters p <- 100 n <- 40 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) # PSGD Ensemble output <- PSGD(x = x.train, y = y.train, n_models = 5, model_type = c("Linear", "Logistic")[1], include_intercept = TRUE, split = 3, size = 10, max_iter = 20, cycling_iter = 0) psgd.coef <- coef(output, group_index = 1:output$n_models) psgd.predictions <- predict(output, newx = x.test, group_index = 1:output$n_models) mean((y.test - psgd.predictions)^2)/sigma.epsilon^2