In samlahiry/hw2: Combining functions of hw2 in a single package

knitr::opts_chunk$set(
  collapse = TRUE,
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This package has three functions.

1. solve_ols() - This function solves linear systems like Ax=b where A is a square matrix by one of the three methods - Gauss, Jacobi or Jacobi-parallel.

2. algo_leverage() - This function estimates the coefficients of a linear regression by subsampling.

3. elnet_coord() - This function estimates the coefficients of a high dimensional linear regression with elastic net penalty using coordinate descent algorithm.

solve_ols()

Usage

solve_ols(A,b,method,tol,maxiter,core)

Arguments

A matrix of the system to be solved.

b vector of the system to be solved.

method "Gauss", "Jacobi" or "Jacobi parallel".

tol a positive number denoting the tolerance level of relative errors (default 1e-10).

maxitermaximum number of iterations (default 10000).

core number of core used for parallel computing (only valid for Jacobi Parallel and default=3).

Value

Solution of the system

Example

library(hw2)
#creating the matrix and vector as given in HW1 but with samller n
n=10
alpha=3
D=alpha*diag(n)
L=matrix(0,n,n)
U=matrix(0,n,n)
for(i in 1:(n-1))
{
L[i+1,i]=-1
U[i,i+1]=-1
}

v=rep(c(1,0),n/2)
A=L+D+U
b=A%*%v

solve_ols(A,b,"Gauss")

algo_leverage()

Usage

algo_leverage(X,y,r,type)

Arguments

X design matrix

y response vector

r number of subsamples

type "unif" denoting uniform weightage or "lev" denoting leverage weightage (default uniform)

Value

Coefficient of the regression

Example

library(hw2)
#creating the example as in hw1
r=100
x=rt(500,6)
y=-x+rnorm(500)
X=as.matrix(x)

algo_leverage(X,y,r)

elnet_coord()

Usage

elnet_coord(y,X,Lambda,alpha,beta_init,iterlength)

Arguments

y The response vector.

X Design matrix

Lambda Sequence of penalizing weights

alpha weightage on L_1 norm

beta_init initial coefficient vector (default rep(0,ncol(X)) - the zero vector )

iterlength no. of iteration of the coordinate descent algorithm (default = 1000)

Value

Solution path - A matrix of dimension (length(Lambda),ncol(X)) where each row gives the coefficient vector for a fixed Lambda.

Example

library(hw2)
#creating the example as in hw1
  #data simulation
Sigma=diag(20)
Sigma[1,2]=Sigma[2,1]=Sigma[5,6]=Sigma[6,5]=0.8
library(MASS)
X=mvrnorm(n,rep(0,20),Sigma)
beta=c(c(2,0,-2,0,1,0,-1),rep(0,13))
y=X%*%beta+rnorm(n)

elnet_coord(y,X,seq(0,0.5,length=10),0.5)

samlahiry/hw2 documentation built on May 25, 2019, 12:43 a.m.