ProxGrad {CPGLIB}

Generalized Linear Models via Proximal Gradients

Description

ProxGrad computes the coefficients for generalized linear models using proximal gradients.

Usage

ProxGrad(
  x,
  y,
  glm_type = c("Linear", "Logistic")[1],
  include_intercept = TRUE,
  alpha_s = 3/4,
  lambda_sparsity,
  tolerance = 1e-08,
  max_iter = 1e+05
)

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" or "Logistic" . Default is "Linear".

include_intercept

Argument to determine whether there is an intercept. Default is TRUE.

alpha_s

Elastic net mixing parmeter. Default is 3/4.

lambda_sparsity

Sparsity tuning parameter value.

tolerance

Convergence criteria for the coefficients. Default is 1e-8.

max_iter

Maximum number of iterations in the algorithm. Default is 1e5.

Value

An object of class ProxGrad.

Author(s)

Anthony-Alexander Christidis, [e-mail]

See Also

coef.ProxGrad, predict.ProxGrad

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)
# 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)

# ProxGrad - Single Group
proxgrad.out <- ProxGrad(x.train, y.train,
                         glm_type = "Logistic",
                         include_intercept = TRUE,
                         alpha_s = 3/4,
                         lambda_sparsity = 0.01, 
                         tolerance = 1e-5, max_iter = 1e5)

# Predictions
proxgrad.prob <- predict(proxgrad.out, newx = x.test, type = "prob")
proxgrad.class <- predict(proxgrad.out, newx = x.test, type = "class")
plot(prob.test, proxgrad.prob, pch = 20)
abline(h = 0.5,v = 0.5)
mean((prob.test-proxgrad.prob)^2)
mean(abs(y.test-proxgrad.class))