Package 'SplitGLM' reference manual

Title:	Split Generalized Linear Models
Description:	Functions to compute split generalized linear models. The approach fits generalized linear models that split the covariates into groups. The optimal split of the variables into groups and the regularized estimation of the coefficients are performed by minimizing an objective function that encourages sparsity within each group and diversity among them. Example applications can be found in Christidis et al. (2021) <arXiv:2102.08591>.
Authors:	Anthony Christidis [aut, cre], Stefan Van Aelst [aut], Ruben Zamar [aut]
Maintainer:	Anthony Christidis <[email protected]>
License:	GPL (>= 2)
Version:	1.0.5
Built:	2024-10-18 06:38:35 UTC
Source:	CRAN

Coefficients for cv.SplitGLM Object

Description

coef.cv.SplitGLM returns the coefficients for a cv.SplitGLM object.

Usage

## S3 method for class 'cv.SplitGLM'
coef(object, group_index = NULL, ...)
## S3 method for class 'cv.SplitGLM'
coef(object, group_index = NULL, ...)

Arguments

`object`	An object of class cv.SplitGLM.
`group_index`	The group for which to return the coefficients. Default is the ensemble coefficients.
`...`	Additional arguments for compatibility.

Value

The coefficients for the cv.SplitGLM object.

Author(s)

Anthony-Alexander Christidis, [email protected]

Examples


# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - CV (Multiple Groups)
split.out <- cv.SplitGLM(x.train, y.train,
                         glm_type="Logistic",
                         G=10, include_intercept=TRUE,
                         alpha_s=3/4, alpha_d=1,
                         n_lambda_sparsity=50, n_lambda_diversity=50,
                         tolerance=1e-3, max_iter=1e3,
                         n_folds=5,
                         active_set=FALSE,
                         n_threads=1)
split.coef <- coef(split.out)
# Predictions
split.prob <- predict(split.out, newx=x.test, type="prob", group_index=NULL)
split.class <- predict(split.out, newx=x.test, type="class", group_index=NULL)
plot(prob.test, split.prob, pch=20)
abline(h=0.5,v=0.5)
mean((prob.test-split.prob)^2)
mean(abs(y.test-split.class))



# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - CV (Multiple Groups)
split.out <- cv.SplitGLM(x.train, y.train,
                         glm_type="Logistic",
                         G=10, include_intercept=TRUE,
                         alpha_s=3/4, alpha_d=1,
                         n_lambda_sparsity=50, n_lambda_diversity=50,
                         tolerance=1e-3, max_iter=1e3,
                         n_folds=5,
                         active_set=FALSE,
                         n_threads=1)
split.coef <- coef(split.out)
# Predictions
split.prob <- predict(split.out, newx=x.test, type="prob", group_index=NULL)
split.class <- predict(split.out, newx=x.test, type="class", group_index=NULL)
plot(prob.test, split.prob, pch=20)
abline(h=0.5,v=0.5)
mean((prob.test-split.prob)^2)
mean(abs(y.test-split.class))

Coefficients for SplitGLM Object

Description

coef.SplitGLM returns the coefficients for a SplitGLM object.

Usage

## S3 method for class 'SplitGLM'
coef(object, group_index = NULL, ...)
## S3 method for class 'SplitGLM'
coef(object, group_index = NULL, ...)

Arguments

`object`	An object of class SplitGLM.
`group_index`	The group for which to return the coefficients. Default is the ensemble.
`...`	Additional arguments for compatibility.

Value

The coefficients for the SplitGLM object.

Author(s)

Anthony-Alexander Christidis, [email protected]

Examples


# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - CV (Multiple Groups)
split.out <- SplitGLM(x.train, y.train,
                      glm_type="Logistic",
                      G=10, include_intercept=TRUE,
                      alpha_s=3/4, alpha_d=1,
                      lambda_sparsity=1, lambda_diversity=1,
                      tolerance=1e-3, max_iter=1e3,
                      active_set=FALSE)
split.coef <- coef(split.out)
# Predictions
split.prob <- predict(split.out, newx=x.test, type="prob", group_index=NULL)
split.class <- predict(split.out, newx=x.test, type="class", group_index=NULL)
plot(prob.test, split.prob, pch=20)
abline(h=0.5,v=0.5)
mean((prob.test-split.prob)^2)
mean(abs(y.test-split.class))



# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - CV (Multiple Groups)
split.out <- SplitGLM(x.train, y.train,
                      glm_type="Logistic",
                      G=10, include_intercept=TRUE,
                      alpha_s=3/4, alpha_d=1,
                      lambda_sparsity=1, lambda_diversity=1,
                      tolerance=1e-3, max_iter=1e3,
                      active_set=FALSE)
split.coef <- coef(split.out)
# Predictions
split.prob <- predict(split.out, newx=x.test, type="prob", group_index=NULL)
split.class <- predict(split.out, newx=x.test, type="class", group_index=NULL)
plot(prob.test, split.prob, pch=20)
abline(h=0.5,v=0.5)
mean((prob.test-split.prob)^2)
mean(abs(y.test-split.class))

Cross Validation - Split Generalized Linear Model

Description

cv.SplitGLM performs the CV procedure for split generalized linear models.

Usage

cv.SplitGLM(
  x,
  y,
  glm_type = "Linear",
  G = 10,
  include_intercept = TRUE,
  alpha_s = 3/4,
  alpha_d = 1,
  n_lambda_sparsity = 50,
  n_lambda_diversity = 50,
  tolerance = 0.001,
  max_iter = 1e+05,
  n_folds = 10,
  active_set = FALSE,
  full_diversity = FALSE,
  n_threads = 1
)
cv.SplitGLM(
  x,
  y,
  glm_type = "Linear",
  G = 10,
  include_intercept = TRUE,
  alpha_s = 3/4,
  alpha_d = 1,
  n_lambda_sparsity = 50,
  n_lambda_diversity = 50,
  tolerance = 0.001,
  max_iter = 1e+05,
  n_folds = 10,
  active_set = FALSE,
  full_diversity = FALSE,
  n_threads = 1
)

Arguments

`x`	Design matrix.
`y`	Response vector.
`glm_type`	Description of the error distribution and link function to be used for the model. Must be one of "Linear", "Logistic", "Gamma" or "Poisson".
`G`	Number of groups into which the variables are split. Can have more than one value.
`include_intercept`	Boolean variable to determine if there is intercept (default is TRUE) or not.
`alpha_s`	Elastic net mixing parmeter. Default is 3/4.
`alpha_d`	Mixing parameter for diversity penalty. Default is 1.
`n_lambda_sparsity`	Number of candidates for the sparsity penalty parameter. Default is 100.
`n_lambda_diversity`	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.
`active_set`	Active set convergence for the algorithm. Default is FALSE.
`full_diversity`	Full diversity between the groups. Default is FALSE.
`n_threads`	Number of threads. Default is 1.

Value

An object of class cv.SplitGLM.

Author(s)

Anthony-Alexander Christidis, [email protected]

Examples


# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - CV (Multiple Groups)
split.out <- cv.SplitGLM(x.train, y.train,
                         glm_type="Logistic",
                         G=10, include_intercept=TRUE,
                         alpha_s=3/4, alpha_d=1,
                         n_lambda_sparsity=50, n_lambda_diversity=50,
                         tolerance=1e-3, max_iter=1e3,
                         n_folds=5,
                         active_set=FALSE,
                         n_threads=1)
split.coef <- coef(split.out)
# Predictions
split.prob <- predict(split.out, newx=x.test, type="prob", group_index=NULL)
split.class <- predict(split.out, newx=x.test, type="class", group_index=NULL)
plot(prob.test, split.prob, pch=20)
abline(h=0.5,v=0.5)
mean((prob.test-split.prob)^2)
mean(abs(y.test-split.class))



# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - CV (Multiple Groups)
split.out <- cv.SplitGLM(x.train, y.train,
                         glm_type="Logistic",
                         G=10, include_intercept=TRUE,
                         alpha_s=3/4, alpha_d=1,
                         n_lambda_sparsity=50, n_lambda_diversity=50,
                         tolerance=1e-3, max_iter=1e3,
                         n_folds=5,
                         active_set=FALSE,
                         n_threads=1)
split.coef <- coef(split.out)
# Predictions
split.prob <- predict(split.out, newx=x.test, type="prob", group_index=NULL)
split.class <- predict(split.out, newx=x.test, type="class", group_index=NULL)
plot(prob.test, split.prob, pch=20)
abline(h=0.5,v=0.5)
mean((prob.test-split.prob)^2)
mean(abs(y.test-split.class))

Plot of coefficients paths for cv.SplitGLM Object

Description

plot.cv.SplitGLM returns the coefficients for a cv.SplitGLM object.

Usage

## S3 method for class 'cv.SplitGLM'
plot(
  x,
  group_index = NULL,
  plot_type = c("Coef", "CV-Error")[1],
  active_only = TRUE,
  path_type = c("Log-Lambda", "L1-Norm")[1],
  labels = TRUE,
  ...
)
## S3 method for class 'cv.SplitGLM'
plot(
  x,
  group_index = NULL,
  plot_type = c("Coef", "CV-Error")[1],
  active_only = TRUE,
  path_type = c("Log-Lambda", "L1-Norm")[1],
  labels = TRUE,
  ...
)

Arguments

`x`	An object of class cv.SplitGLM.
`group_index`	The group for which to return the coefficients. Default is the ensemble coefficients.
`plot_type`	Plot of coefficients, "Coef" (default), or cross-validated error or deviance, "CV-Error".
`active_only`	Only include the variables selected in final model (default is TRUE).
`path_type`	Plot of coefficients paths as a function of either "Log-Lambda" (default) or "L1-Norm".
`labels`	Include the labels of the variables (default is FALSE).
`...`	Additional arguments for compatibility.

Value

The coefficients for the cv.SplitGLM object.

Author(s)

Anthony-Alexander Christidis, [email protected]

Examples


# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - CV (Multiple Groups)
split.out <- cv.SplitGLM(x.train, y.train,
                         glm_type="Logistic",
                         G=10, include_intercept=TRUE,
                         alpha_s=3/4, alpha_d=1,
                         n_lambda_sparsity=50, n_lambda_diversity=50,
                         tolerance=1e-3, max_iter=1e3,
                         n_folds=5,
                         active_set=FALSE,
                         n_threads=1)
                         
# Plot of coefficients paths (function of Log-Lambda)
plot(split.out, plot_type="Coef", path_type="Log-Lambda", group_index=1, labels=FALSE)

# Plot of coefficients paths (function of L1-Norm)
plot(split.out, plot_type="Coef", path_type="L1-Norm", group_index=1, labels=FALSE)

# Plot of CV error
plot(split.out, plot_type="CV-Error")



# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - CV (Multiple Groups)
split.out <- cv.SplitGLM(x.train, y.train,
                         glm_type="Logistic",
                         G=10, include_intercept=TRUE,
                         alpha_s=3/4, alpha_d=1,
                         n_lambda_sparsity=50, n_lambda_diversity=50,
                         tolerance=1e-3, max_iter=1e3,
                         n_folds=5,
                         active_set=FALSE,
                         n_threads=1)
                         
# Plot of coefficients paths (function of Log-Lambda)
plot(split.out, plot_type="Coef", path_type="Log-Lambda", group_index=1, labels=FALSE)

# Plot of coefficients paths (function of L1-Norm)
plot(split.out, plot_type="Coef", path_type="L1-Norm", group_index=1, labels=FALSE)

# Plot of CV error
plot(split.out, plot_type="CV-Error")

Predictions for cv.SplitGLM Object

Description

predict.cv.SplitGLM returns the predictions for a SplitGLM object.

Usage

## S3 method for class 'cv.SplitGLM'
predict(object, newx, group_index = NULL, type = c("prob", "class")[1], ...)
## S3 method for class 'cv.SplitGLM'
predict(object, newx, group_index = NULL, type = c("prob", "class")[1], ...)

Arguments

`object`	An object of class cv.SplitGLM.
`newx`	New data for predictions.
`group_index`	The group for which to return the coefficients. Default is the ensemble.
`type`	The type of predictions for binary response. Options are "prob" (default) and "class".
`...`	Additional arguments for compatibility.

Value

The predictions for the cv.SplitGLM object.

Author(s)

Anthony-Alexander Christidis, [email protected]

Examples


# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - CV (Multiple Groups)
split.out <- cv.SplitGLM(x.train, y.train,
                         glm_type="Logistic",
                         G=10, include_intercept=TRUE,
                         alpha_s=3/4, alpha_d=1,
                         n_lambda_sparsity=50, n_lambda_diversity=50,
                         tolerance=1e-3, max_iter=1e3,
                         n_folds=5,
                         active_set=FALSE,
                         n_threads=1)
split.coef <- coef(split.out)
# Predictions
split.prob <- predict(split.out, newx=x.test, type="prob", group_index=NULL)
split.class <- predict(split.out, newx=x.test, type="class", group_index=NULL)
plot(prob.test, split.prob, pch=20)
abline(h=0.5,v=0.5)
mean((prob.test-split.prob)^2)
mean(abs(y.test-split.class))



# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - CV (Multiple Groups)
split.out <- cv.SplitGLM(x.train, y.train,
                         glm_type="Logistic",
                         G=10, include_intercept=TRUE,
                         alpha_s=3/4, alpha_d=1,
                         n_lambda_sparsity=50, n_lambda_diversity=50,
                         tolerance=1e-3, max_iter=1e3,
                         n_folds=5,
                         active_set=FALSE,
                         n_threads=1)
split.coef <- coef(split.out)
# Predictions
split.prob <- predict(split.out, newx=x.test, type="prob", group_index=NULL)
split.class <- predict(split.out, newx=x.test, type="class", group_index=NULL)
plot(prob.test, split.prob, pch=20)
abline(h=0.5,v=0.5)
mean((prob.test-split.prob)^2)
mean(abs(y.test-split.class))

Predictions for SplitGLM Object

Description

predict.SplitGLM returns the predictions for a SplitGLM object.

Usage

## S3 method for class 'SplitGLM'
predict(object, newx, group_index = NULL, type = c("prob", "class")[1], ...)
## S3 method for class 'SplitGLM'
predict(object, newx, group_index = NULL, type = c("prob", "class")[1], ...)

Arguments

`object`	An object of class SplitGLM.
`newx`	New data for predictions.
`group_index`	The group for which to return the coefficients. Default is the ensemble.
`type`	The type of predictions for binary response. Options are "prob" (default) and "class".
`...`	Additional arguments for compatibility.

Value

The predictions for the SplitGLM object.

Author(s)

Anthony-Alexander Christidis, [email protected]

Examples


# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - CV (Multiple Groups)
split.out <- SplitGLM(x.train, y.train,
                      glm_type="Logistic",
                      G=10, include_intercept=TRUE,
                      alpha_s=3/4, alpha_d=1,
                      lambda_sparsity=1, lambda_diversity=1,
                      tolerance=1e-3, max_iter=1e3,
                      active_set=FALSE)
split.coef <- coef(split.out)
# Predictions
split.prob <- predict(split.out, newx=x.test, type="prob", group_index=NULL)
split.class <- predict(split.out, newx=x.test, type="class", group_index=NULL)
plot(prob.test, split.prob, pch=20)
abline(h=0.5,v=0.5)
mean((prob.test-split.prob)^2)
mean(abs(y.test-split.class))



# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - CV (Multiple Groups)
split.out <- SplitGLM(x.train, y.train,
                      glm_type="Logistic",
                      G=10, include_intercept=TRUE,
                      alpha_s=3/4, alpha_d=1,
                      lambda_sparsity=1, lambda_diversity=1,
                      tolerance=1e-3, max_iter=1e3,
                      active_set=FALSE)
split.coef <- coef(split.out)
# Predictions
split.prob <- predict(split.out, newx=x.test, type="prob", group_index=NULL)
split.class <- predict(split.out, newx=x.test, type="class", group_index=NULL)
plot(prob.test, split.prob, pch=20)
abline(h=0.5,v=0.5)
mean((prob.test-split.prob)^2)
mean(abs(y.test-split.class))

Split Generalized Linear Model

Description

SplitGLM performs computes the coefficients for split generalized linear models.

Usage

SplitGLM(
  x,
  y,
  glm_type = "Linear",
  G = 10,
  include_intercept = TRUE,
  alpha_s = 3/4,
  alpha_d = 1,
  lambda_sparsity,
  lambda_diversity,
  tolerance = 0.001,
  max_iter = 1e+05,
  active_set = FALSE
)
SplitGLM(
  x,
  y,
  glm_type = "Linear",
  G = 10,
  include_intercept = TRUE,
  alpha_s = 3/4,
  alpha_d = 1,
  lambda_sparsity,
  lambda_diversity,
  tolerance = 0.001,
  max_iter = 1e+05,
  active_set = FALSE
)

Arguments

`x`	Design matrix.
`y`	Response vector.
`glm_type`	Description of the error distribution and link function to be used for the model. Must be one of "Linear", "Logistic", "Gamma" or "Poisson".
`G`	Number of groups into which the variables are split. Can have more than one value.
`include_intercept`	Boolean variable to determine if there is intercept (default is TRUE) or not.
`alpha_s`	Elastic net mixing parmeter. Default is 3/4.
`alpha_d`	Mixing parameter for diversity penalty. Default is 1.
`lambda_sparsity`	Sparsity tuning parameter value.
`lambda_diversity`	Diversity tuning parameter value.
`tolerance`	Convergence criteria for the coefficients. Default is 1e-3.
`max_iter`	Maximum number of iterations in the algorithm. Default is 1e5.
`active_set`	Active set convergence for the algorithm. Default is FALSE.

Value

An object of class SplitGLM.

Author(s)

Anthony-Alexander Christidis, [email protected]

Examples


# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - Multiple Groups
split.out <- SplitGLM(x.train, y.train,
                      glm_type="Logistic",
                      G=10, include_intercept=TRUE,
                      alpha_s=3/4, alpha_d=1,
                      lambda_sparsity=1, lambda_diversity=1,
                      tolerance=1e-3, max_iter=1e3,
                      active_set=FALSE)
split.coef <- coef(split.out)
# Predictions
split.prob <- predict(split.out, newx=x.test, type="prob", group_index=NULL)
split.class <- predict(split.out, newx=x.test, type="class", group_index=NULL)
plot(prob.test, split.prob, pch=20)
abline(h=0.5,v=0.5)
mean((prob.test-split.prob)^2)
mean(abs(y.test-split.class))



# Data simulation
set.seed(1)
n <- 50
N <- 2000
p <- 1000
beta.active <- c(abs(runif(p, 0, 1/2))*(-1)^rbinom(p, 1, 0.3))
# Parameters
p.active <- 100
beta <- c(beta.active[1:p.active], rep(0, p-p.active))
Sigma <- matrix(0, p, p)
Sigma[1:p.active, 1:p.active] <- 0.5
diag(Sigma) <- 1

# Train data
x.train <- mvnfast::rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- exp(x.train %*% beta)/
              (1+exp(x.train %*% beta))
y.train <- rbinom(n, 1, prob.train)
mean(y.train)
# Test data
x.test <- mvnfast::rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- exp(x.test %*% beta)/
             (1+exp(x.test %*% beta))
y.test <- rbinom(N, 1, prob.test)
mean(y.test)

# SplitGLM - Multiple Groups
split.out <- SplitGLM(x.train, y.train,
                      glm_type="Logistic",
                      G=10, include_intercept=TRUE,
                      alpha_s=3/4, alpha_d=1,
                      lambda_sparsity=1, lambda_diversity=1,
                      tolerance=1e-3, max_iter=1e3,
                      active_set=FALSE)
split.coef <- coef(split.out)
# Predictions
split.prob <- predict(split.out, newx=x.test, type="prob", group_index=NULL)
split.class <- predict(split.out, newx=x.test, type="class", group_index=NULL)
plot(prob.test, split.prob, pch=20)
abline(h=0.5,v=0.5)
mean((prob.test-split.prob)^2)
mean(abs(y.test-split.class))

Package 'SplitGLM'

Help Index

Coefficients for cv.SplitGLM Object

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Coefficients for SplitGLM Object

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Cross Validation - Split Generalized Linear Model

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Plot of coefficients paths for cv.SplitGLM Object

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Predictions for cv.SplitGLM Object

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Predictions for SplitGLM Object

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Split Generalized Linear Model

Description

Usage

Arguments

Value

Author(s)

See Also

Examples