ProxGrad {CPGLIB} R Documentation

## 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, anthony.christidis@stat.ubc.ca

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
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)