R/linear_gd_optim.R

In FedericoCortese/R4DScm:

#' Linear Gradient Descend
#'
#' This function  computes the vector of parameters in a linear regression model via the Gradient Descend Method.
#'
#' @param b_pre vector of initial parameters
#' @param X Covariates Matrix: each column contains observations for each covariate.
#' @param y Response variable observations
#' @param tol Tolerance level for the optimization process, the default is 0.001.
#' @param maxit Maximum iterations number
#' @param stepsize The value for the stepsize in the equation of the gradient descend
#'
#' @return A list containing the fitted values for the beta vector and the number of iterations performed
#'
#' @examples
#' set.seed(8675309)
#' n = 1000
#' x1 = rnorm(n)
#' x2 = rnorm(n)
#' y = 1 + .5*x1 + .2*x2 + rnorm(n)
#' X=cbind(x1,x2)

#' b_pre=c(0,0,0)
#' linear_gd_optim(b_pre,X,y)
#' @export
linear_gd_optim <- function(b_pre,             # beta(0)
                            X,               # data predictors
                            y,               # response variable
                            tol=1e-3,  # tolerance
                            maxit=1000,      # max iteration, not to run forever
                            stepsize=1e-3#,   # stepsize parameter
                            #verbose=F
) {

  X <- cbind(1, X)

  k=length(b_pre)
  gradient=sapply(1:k, function(i) 2*mean((X%*%b_pre-y)*X[,i]))


  b_post=b_pre-gradient*stepsize
  diff <- tol + 1
  iter <- 0

  while (diff > tol & iter <= maxit) {
    b_pre=b_post
    gradient=sapply(1:k, function(i) 2*mean((X%*%b_pre-y)*X[,i]))

    b_post=b_pre-gradient*stepsize
    iter=iter+1
    diff=max(abs(b_pre-b_post))
  }

  return(list(param=b_post,iter=iter))

}