In xysxu/hwyx:

Package needed before using

library(foreach)
library(iterators)
library(Rlinsolve)
library(pracma)
library(parallel)
library(gdata)
library(doParallel)
library(MASS)
#my package
library(hwyx)

library(hwyx)
library(foreach)
library(iterators)
library(Rlinsolve)
library(pracma)
library(parallel)
library(gdata)
library(doParallel)
library(MASS)

Weighted leveraging algorithm

This algorithm attempts to approximate the linear regression coefficient $\hat{β}$ in a dataset of sample size n using only a randomly selected subset of size $r< n$. Selecting r samples uniformly at random $(\pi_i = 1/n)$ often produces biased estimate, while selecting samples with probability proportional to their leverage scores $\pi_{i} \propto h_{i}$ largely alleviates this problem.

Example

e = rnorm(500,0,1)
x = rt(500, df = 6)
y = -x+e
algo_leverage(x, y, r=10, methods="UNIF")

Iterative Methods for Solving Linear System of Equations

In this function, we basically can apply Gauss-Seidel, Jacobi (sequential) and Jacobi (parallel) to do iteration methods to solve linear models. This function provides three options in the iterative methods for the user. In view of the convergence, the function will automatically examine the convergence and return the results only the methods are convergent urder user's case.

Example

a1=2
n1=10
D1= matrix(0, n1, n1)
L1= matrix(0, n1, n1)
U1= matrix(0, n1, n1)
for(i in 1:n1-1){
D1[i,i]=a1;
L1[i,i+1]=-1;
U1[i+1,i]=-1
 }
D1[n1,n1]=a1
A=D1+L1+U1
m1=n1/2
v=rep(c(1,0),times=m1)
b=A%*%v
p=2
solve_ols(A, b, tol = 1e-10, methods="JS", p=2)

Coordinate Descent for Elastic Net

we derived a coordinate descent algorithm for finding a solution to the lasso problem. The goal of this exercise is to derive and implement a similar algorithm for solving an elastic net problem $$\min {\beta \in \mathbb{R}^{p}} \frac{1}{n} \sum{i=1}^{n}\left(y_{i}-x_{i}^{\top} \beta\right)^{2}+\lambda\left[(1-\alpha)\|\beta\|{2}^{2}+\alpha\|\beta\|{1}\right]$$

Example

p = 20
n = 100
x=matrix(0,nrow = n, ncol = p)
beta=c(2,0,-2,0,1,0,-1,0,rep(0,12))
x[,1:2] = mvrnorm(n, mu = c(0,0), Sigma = matrix(c(1,0.8,0.8,1), ncol = 2))
x[,5:6] = mvrnorm(n, mu = c(0,0), Sigma = matrix(c(1,0.8,0.8,1), ncol = 2))
x[,3:4] = mvrnorm(n, mu = c(0,0), Sigma = matrix(c(1,0,0,1), ncol = 2))
for(i in 7:p){
x[,i] = rnorm(n, mean = 0, sd = 1)
}
e = rnorm(n, mean = 0, sd = 1)
y = x%*%beta+e
elnet_coord(x, y, lambda=1, alpha=0.5, tol=1e-6)

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

xysxu/hwyx documentation built on June 6, 2019, 7:55 a.m.