Split Generalized Linear Models

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) .

SplitGLM

This package provides functions for fitting split generalized linear models.

Installation

You can install the stable version on R CRAN.

install.packages("SplitGLM", dependencies = TRUE)

You can install the development version from GitHub

library(devtools)
devtools::install_github("AnthonyChristidis/SplitGLM")

Usage

# Required Libraries
library(mvnfast)

# Sigmoid function
sigmoid <- function(t){
  return(exp(t)/(1+exp(t)))
}

# 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 <- rmvn(n, mu = rep(0, p), sigma = Sigma) 
prob.train <- sigmoid(x.train %*% beta)
y.train <- rbinom(n, 1, prob.train)

# Test data
x.test <- rmvn(N, mu = rep(0, p), sigma = Sigma)
prob.test <- sigmoid(x.test %*% beta + offset)
y.test <- rbinom(N, 1, prob.test)
mean(y.test)
sp.sen.par <- y.test==0

# SplitGLM - CV (Multiple Groups)
split.out <- cv.SplitGLM(x.train, y.train,
                         type="Logistic",
                         G=10, include_intercept=TRUE,
                         alpha_s=3/4,
                         n_lambda_sparsity=100, n_lambda_diversity=100,
                         tolerance=1e-3, max_iter=1e3,
                         n_folds=5,
                         active_set=FALSE,
                         full_diversity=TRUE,
                         n_threads=1)

# Coefficients
split.coef <- coef(split.out)

# Predictions
split.prob <- predict(split.out, newx=x.test, type="prob")

# Plot of output
plot(prob.test, split.prob, pch=20)
abline(h=0.5,v=0.5)

# MR
split.class <- predict(split.out, newx=x.test, type="class")
mean(abs(y.test-split.class))

License

This package is free and open source software, licensed under GPL (>= 2).