In sophiaycl/6520HW2: STSCI6520HW

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
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Homework R Package

Download and install the package use devtools:

library(devtools)
install_github("sophiaycl/HW2")

Load the package with the usual R commands:

library(HW2)

HW2 has three functions:

A. Ordinary least sqaure solver by iterative methods

To solve $x$ for a linear system $Ax = b$, the function has the basic form of:

solve_ols(A, b, ncores = 1, type ='GS', iterNum = 10000)

$A$ is required to be a $n \times n$ square invertible matrix, $b$ is a vector with the same dimension $n$.

An example is shown here.

D = diag(rep(10, 10))
N = matrix(rnorm(50), ncol = 10)
A = D + N
b = runif(10)

x_JC = solve_ols(A, b, type = 'JC', iterNum = 500)
x_GS = solve_ols(A, b, iterNum = 500)
print(cbind(x_JC, x_GS))

B. Leverage subsampling regression

$Y = X \beta + E$.

An example is given as:

  n = 500; p = 6; r = 30

  X = matrix(rnorm(n * p), nrow = n)
  true.beta = 3 * runif(p)

  y = X %*% true.beta + rnorm(n)
  beta.unif = algo_leverage(X, y, sampSize = r, sampleType = 'Unif')
  beta.lev = algo_leverage(X, y, sampSize = r, sampleType = 'Lev')

  print(cbind(beta.unif, beta.lev))

C. Elastic net regression

A similar example is given as:

  n = 300; p = 100
  X = matrix(rnorm(n * p), nrow = n)
  true.beta = 3 * runif(p)
  Y = X %*% true.beta + rnorm(n)

  beta.elnet = elnet_coord(X, Y, a = 0.5, lambda = 5, GLMNET = FALSE)
  beta.glm = elnet_coord(X, Y, a = 0.5, lambda = 5, GLMNET = TRUE)