In stevebroll/stsci6520hw2: OLS, Algorithmic Leveraging, and Elastic Net

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
  )

library(stsci6520hw2)

elnet_coord

Data generation

beta = c(2,0,-2,0,1,0,-1,rep(0,13))
covar = diag(1,20)
covar[1,2] = covar[2,1] = covar[5,6] = covar[6,5] = .8
x = MASS::mvrnorm(20, rep(0, 20), covar)
y = x %*% beta + rnorm(20, 0, 1)

Default Settings, alpha = 0, 0.5, 1

alpha = c(0, 0.5, 1)
for(a in alpha){
  cat(paste('alpha = ', a, '\n'))
  elfit = elnet_coord(x, y, alpha = a, lambda = 0.1, tol = 1e-04)
  plot(elfit$Beta, ylab = 'Beta', main = paste('alpha = ', a, 'lambda = ', .1), type = 'l', ylim = c(-2,2))
}

Changing lambda and tolerance

elfit = elnet_coord(x, y, alpha = .5, lambda = .01, tol = 1e-02)
  plot(elfit$Beta, ylab = 'Beta', main = paste('alpha = ', .5, 'lambda = ', .01), type = 'l', ylim = c(-2,2))

algo_leverage

Data Generation, x as Vector

x = rt(500, 6)
y = -x + rnorm(500)

Default Settings with subset_size = 100

algo_leverage(x, y, subset_size = 100, num_sample = 500, method = 'both')

Output Betas from Single Run of Leverage Sampling

algo_leverage(x, y, subset_size = 100, method = 'leverage')

algo_leverage(x, y, subset_size = 100, method = 'uniform')

Data Generation, x as Matrix

x = MASS::mvrnorm(500, mu = rep(0,5), Sigma = diag(1:5))
beta = c(-2,0,2,0,1)
y = x %*% beta + rnorm(500)

Single Run comparison with subset_size = 50

algo_leverage(x, y, subset_size = 50, num_sample = 1, method = 'both')

solve_ols

Data Generation

A = diag(2, nrow = 20)
A[abs(row(A) -col(A)) == 1] = -1
b = A%*%(0.5*1:20)

Default Sequential Gauss-Seidel

t(solve_ols(A, b, iter = 5000))

Sequential Jacobi with 1000 iterations

t(solve_ols(A, b, method = 'jacobi', iter = 1000))

Sequential Jacobi with 1000 iterations

t(solve_ols(A, b, method = 'jacobi', iter = 2000))

Parallel Jacobi with 10 cores

library(foreach); library(doParallel); library(parallel)

t(solve_ols(A, b, method = 'parallel', iter = 2000, ncores = 2))

stevebroll/stsci6520hw2 documentation built on Dec. 23, 2021, 5:32 a.m.