glm_hw3b: GLM Using First-Order Gradient Descent

In brian-d1018/bis557: Brian's BIS 557 Work

Description

This function solves generalized linear models using only first-order conditions, avoiding the Hessian matrix. This uses the gradient descent algorithm, with either a constant or adaptive step size.

Usage

glm_hw3b(X, y, family, steps, maxiter = 1000, tol = 1e-12)

Arguments

X	Numeric (continuous or categorical) data matrix
y	Response/Target vector
family	Error distribution and link function, such as poisson or Gamma
steps	Step size for each iteration
maxiter	Maximum number of iterations
tol	Tolerance

Value

Estimated beta coefficients

Examples

set.seed(2020)
n <- 3000; p <- 4; maxiter <- 500; steps <- rep(1e-3, maxiter)
X <- cbind(1, matrix(rnorm(n * (p-1)), ncol = p-1))
beta <- c(-1, 0.2, 0.1, 0.3)
y <- rpois(n, lambda = exp(X %*% beta))
glm_hw3b(X, y, family = poisson(link = "log"), steps, maxiter)

set.seed(2020)
steps2 <- 5e-3/(1:maxiter)
glm_hw3b(X, y, family = poisson(link = "log"), steps = steps2, maxiter)

brian-d1018/bis557 documentation built on Dec. 17, 2020, 6:21 p.m.