glm_firstorder: First-Order Method of Generalized Linear Model

In BillyTian/bis557: Package containing assignments, projects or other products in BIS557

Description

This function gives a first-order solution for the GLM maximum likelihood problem using only gradient information, avoiding the Hessian matrix. A comparison of a constant step size and an adaptive one is also included.

Usage

glm_firstorder(form, data, mu_fun, step = "constant", gamma = 1e-06,
  maxit = 1000, tol = 1e-06)

Arguments

form	a formula with the legal format.
data	a dataframe provided by the user.
mu_fun	a specified link function inverse.
step	indicate method, constant or momentum step.
gamma	the learning rate.
maxit	the maximum number of iterations.
tol	the tolerance of the squared difference of beta to show convergence.
data	a dataframe provided by the user.

Value

a list including the coefficient estimates.

Examples

set.seed(1713948)
n <- 1000
truth <- c(4, 0.5, 0.3, 1)
X <- cbind(rep(1,n), matrix(rnorm(3*n), ncol=3))
lambda <- exp(X %*% truth)
Y <- rpois(n, lambda=lambda)
covs <- X[,-1]
q2.data <- data.frame(cbind(Y, covs))
form <- Y ~ .
glm_firstorder(form, q2.data, step="momentum", mu_fun=function(eta) exp(eta))$beta

BillyTian/bis557 documentation built on Dec. 19, 2020, 7:30 a.m.