| Type: | Package |
| Title: | Linear Models for Prediction and Classification using Proximal Operators |
| Version: | 1.1.2 |
| Date: | 2025-06-16 |
| Maintainer: | YingHong Chen <yinghongchen1402@gmail.com> |
| Description: | Implements optimization techniques for Lasso regression, R.Tibshirani(1996)<doi:10.1111/j.2517-6161.1996.tb02080.x> using Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) and Iterative Shrinkage-Thresholding Algorithm (ISTA) based on proximal operators, A.Beck(2009)<doi:10.1137/080716542>. The package is useful for high-dimensional regression problems and includes cross-validation procedures to select optimal penalty parameters. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| Language: | en-US |
| RoxygenNote: | 7.3.2 |
| Suggests: | knitr, rmarkdown, |
| VignetteBuilder: | knitr |
| Imports: | dplyr, EBImage, glmnet |
| NeedsCompilation: | no |
| Packaged: | 2025-06-16 15:44:40 UTC; yingh |
| Author: | YingHong Chen [aut, cre], Ferran Reverter Comes [aut], Esteban Vegas Lozano [aut] |
| Repository: | CRAN |
| Date/Publication: | 2025-06-17 09:00:12 UTC |
rectangular hole in image
Description
creates a rectangular hole in the image with the specified dimensions
Usage
delete_rect(image,i,j,width,height)
Arguments
image |
image to be modified, it has to be a 3D array proceed with readImage function from EBImage package |
i |
row index of the upper left corner of the rectangle |
j |
column index of the upper left corner of the rectangle |
width |
width of the rectangle |
height |
height of the rectangle |
Details
delete_rect
Value
a 3D array with pixels in the hole set to -100 and the rest of the image pixels unchanged
Examples
image<-EBImage::readImage(system.file("extdata", "bird.jpg", package = "ProxReg"))
image_noise<-delete_rect(image,160,160,20,20)
image_noise<-EBImage::Image(image_noise,colormode = "Color")
EBImage::display(image_noise)
image recovery using Lasso regression
Description
predicts the missing pixels in an image using Lasso regression and fills the hole in the image
Usage
inpainting(image,h,stride,i,j,width,height,lambda=0.1,max_iter=50000,
fista=TRUE, verbose=TRUE,ini=0,glmnet=TRUE,noise=TRUE)
Arguments
image |
image to be modified, it has to be a 3D array proceed with readImage function from EBImage package |
h |
size of the patch |
stride |
stride for the patch |
i |
row index of the upper left corner of the rectangle |
j |
column index of the upper left corner of the rectangle |
width |
width of the rectangle |
height |
height of the rectangle |
lambda |
a penalized parameter for the Lasso regression, it is 0.1 by default |
max_iter |
maximum number of iterations, it is 50000 by default |
fista |
fista=TRUE: use FISTA algortihm for the pixel prediction |
verbose |
print the iteration number and the size of the boundary |
ini |
initial value for the coefficients, default is 0 |
glmnet |
use glmnet package for the Lasso regression |
noise |
display the image with the hole, it is TRUE by default |
Details
inpainting
Value
a 3D array with the hole filled by pixels predicted by Lasso regression
Examples
test_img <- EBImage::readImage(system.file("extdata", "bird.jpg", package = "ProxReg"))
image_repaired <- inpainting(
test_img, h = 10, stride = 6, i = 160, j = 160, width = 20, height = 20,
lambda = 0.001, max_iter = 1000, verbose = TRUE, glmnet = TRUE,noise=TRUE)
RGB_repaired<-EBImage::Image(image_repaired,colormode = "Color")
k_fold_cross
Description
k_fold_cross splits the dataset into k parts, and uses k-1 parts to train the model and the remaining part to test the model.
Usage
k_fold_cross(data,k)
Arguments
data |
dataset which will be used for K-Fols Cross Validation |
k |
integer |
Value
a list with two sublists: training set and test set
Examples
df = data.frame("hours"=c(1, 2, 4, 5, 5, 6, 6, 7, 8, 10, 11, 11, 12, 12, 14),
"score"=c(64, 66, 76, 73, 74, 81, 83, 82, 80, 88, 84, 82, 91, 93, 89))
k_fold_cross(df,k=2)
K-Fold Cross validation for L1/L2 regression
Description
the function realizes K-Fold Cross validation for ridge/Lasso regression to help to choose the lambda that minimise the RSS
Usage
l_CV(data,y,x,lambda,k,mode=2,binary=FALSE,step=1000,bound=0.5,fista=TRUE,tol=10^-7)
Arguments
data |
name of the dataset |
y |
name of the dependent variables |
x |
name of the independent variable |
lambda |
a number or a vector of lambda-value to be evaluated in the regression |
k |
integer, which indicates how many training and test set will be splited from the dataset |
mode |
1: ridge regression; 2: lasso regression |
binary |
logical, if TRUE, the dependent variable is binary |
step |
maximum number of steps |
bound |
threshold for binary dependent variable |
fista |
logical, if TRUE, the FISTA algorithm is used |
tol |
tolerance for convergence, it is 10^-7 by default |
Value
the lambda values that minimize the MSE
Examples
l_CV(mtcars,"hp",c("mpg","qsec","disp"),c(0.01,0.1),k=5,mode=2)
Lasso regression with fixed step with FISTA algorithm
Description
the function carries out the Lasso regression using fixed step using FISTA algorithm.
Usage
lasso_fista(data,y,x,lambda,max_step=10000,type="Gaussian",image=TRUE,ini=0.5,tol=10^-7)
Arguments
data |
name of the dataset |
y |
name of the dependent variables |
x |
name of the independent variable |
lambda |
a vector of lambda-value to be evaluated in the regression |
max_step |
maximum number of steps |
type |
type of response variable, by default, it is 'Gaussian' for continuos response and can be modified as 'Binomial' for binary response |
image |
logical, if TRUE, the evolution of errors in term of lambda values will be plotted |
ini |
initial value for the coefficients |
tol |
tolerance for convergence, it is 10^-7 by default |
Details
lasso_fista
Value
A list containing:
coefficients: A matrix where each column represents the estimated regression coefficients for a different lambda value.error_evolution: A numeric vector tracking the error at certain step.num_steps: An integer vector indicating the number of steps in which errors are calculated.
Examples
library("glmnet")
data("QuickStartExample")
test<-as.data.frame(cbind(QuickStartExample$y,QuickStartExample$x))
lasso_fista(test,"V1",colnames(test)[2:21],lambda=0.1,image=TRUE,max_step=1000)
Lasso regression with backtraking line research with FISTA algorithm
Description
the function carries out the Lasso regression using backtraking line research and FISTA algorithm.
Usage
lasso_fista_back(data,y,x,lambda,max_step=10000,tol=10^-7,
type="Gaussian",ini=0.5,image=TRUE)
Arguments
data |
name of the dataset |
y |
name of the dependent variables |
x |
name of the independent variable |
lambda |
a vector of lambda-value to be evaluated in the regression |
max_step |
maximum number of steps |
tol |
tolerance for convergence, it is 10^-7 by default |
type |
type of response variable, by default, it is 'Gaussian' for continuos response and can be modified as 'Binomial' for binary response |
ini |
initial value for the coefficients, default is 0.5 |
image |
plots the evolution of errors in term of lambda values |
Details
lasso_fista_back
Value
A list containing:
coefficients: A matrix where each column represents the estimated regression coefficients for a different lambda value.error_evolution: A numeric vector tracking the error at certain step.num_steps: An integer vector indicating the number of steps in which errors are calculated.
Examples
library("glmnet")
data("QuickStartExample")
test<-as.data.frame(cbind(QuickStartExample$y,QuickStartExample$x))
lasso_fista_back(test,"V1",colnames(test)[2:21],lambda=0.1,image=TRUE,type='Gaussian',max_step=1000)
Lasso regression with fixed step with ISTA algorithm
Description
the function carries out the Lasso regression using fixed step using ISTA algorithm.
Usage
lasso_ista(data,y,x,lambda,max_step=10000,type="Gaussian",image=TRUE,tol=10^-7,ini=0.5)
Arguments
data |
name of the dataset |
y |
name of the dependent variables |
x |
name of the independent variable |
lambda |
a vector of lambda-value to be evaluated in the regression |
max_step |
maximum number of steps |
type |
type of response variable, by default, it is 'Gaussian' for continuos response and can be modified as 'Binomial' for binary response |
image |
logical, if TRUE, the evolution of errors in term of lambda values will be plotted |
tol |
tolerance for convergence, it is 10^-7 by default |
ini |
initial value for the coefficients |
Details
lasso_ista
Value
A list containing:
coefficients: A matrix where each column represents the estimated regression coefficients for a different lambda value.error_evolution: A numeric vector tracking the error at certain step.num_steps: An integer vector indicating the number of steps in which errors are calculated.
Examples
library("glmnet")
data("QuickStartExample")
test<-as.data.frame(cbind(QuickStartExample$y,QuickStartExample$x))
lasso_ista(test,"V1",colnames(test)[2:21],lambda=0.1,image=TRUE,max_step=1000)
Lasso regression with backtraking line research
Description
the function carries out the Lasso regression using backtraking line research and ISTA algorithm.
Usage
lasso_ista_back(data,y,x,lambda,max_step=10000,tol=10^-7,
type="Gaussian",ini=0.5,image=TRUE)
Arguments
data |
name of the dataset |
y |
name of the dependent variables |
x |
name of the independent variable |
lambda |
a vector of lambda-value to be evaluated in the regression |
max_step |
maximum number of steps |
tol |
tolerance for convergence, it is 10^-7 by default |
type |
type of response variable, by default, it is 'Gaussian' for continuos response and can be modified as 'Binomial' for binary response |
ini |
initial value for the coefficients,dafault is 0.5 |
image |
plots the evolution of errors in term of lambda values |
Details
lasso_ista_back
Value
A list containing:
coefficients: A matrix where each column represents the estimated regression coefficients for a different lambda value.error_evolution: A numeric vector tracking the error at certain step.num_steps: An integer vector indicating the number of steps in which errors are calculated.
Examples
library("glmnet")
data("QuickStartExample")
test<-as.data.frame(cbind(QuickStartExample$y,QuickStartExample$x))
lasso_ista_back(test,"V1",colnames(test)[2:21],lambda=0.1,image=TRUE,type='Gaussian',max_step=100)
Lasso logistic regression for multinomial response variable with fixed step
Description
the function realizes L1-regularized classification for multinomial response variable using ISTA / FISTA algorithm
Usage
lasso_multi(data,y,x,lambda,max_step=10000,image=FALSE,fista=TRUE)
Arguments
data |
name of the dataset |
y |
name of the dependent variables |
x |
name of the independent variable |
lambda |
a number or a vector of lambda-value to be evaluated in the regression |
max_step |
maximum number of steps |
image |
plots the evolution of errors in term of lambda values |
fista |
fista=TRUE: use FISTA algortihm for the multiclass logistic regression; fista=FALSE: use ISTA algortihm |
Details
lasso_multi
Value
A list containing:
coefficients: A matrix where each column represents the estimated regression coefficients for a different lambda value.error_evolution: A numeric vector tracking the error at certain step.num_steps: An integer vector indicating the number of steps in which errors are calculated.
Examples
library(glmnet)
data("MultinomialExample")
x<-MultinomialExample$x
y<-MultinomialExample$y
mult<-as.data.frame(cbind(x,y))
lasso_multi(mult,y="y",x=colnames(mult)[-31],max_step = 1000,lambda=0.01,image=TRUE,fista=TRUE)
Lasso regression with backtraking line research for multinomial response variable
Description
the function carries out the Lasso regression for multinomial response using backtraking line research and FISTA/ISTA algorithm.
Usage
lasso_multi_back(data,y,x,lambda,max_step=10000,image=FALSE,fista=TRUE,tol=10^-7,ini=0)
Arguments
data |
name of the dataset |
y |
name of the dependent variables |
x |
name of the independent variable |
lambda |
a vector of lambda-value to be evaluated in the regression |
max_step |
maximum number of steps |
image |
plots the evolution of errors in term of lambda values |
fista |
fista=TRUE: use FISTA algortihm for the multiclass logistic regression; fista=FALSE: use ISTA algortihm |
tol |
tolerance for the convergence |
ini |
initial value for the coefficients, default is 0 #'@examples library(glmnet) data("MultinomialExample") x<-MultinomialExample$x y<-MultinomialExample$y mult<-as.data.frame(cbind(x,y)) lasso_multi_back(mult,y="y",x=colnames(mult)[-31],max_step = 1000,lambda=0.01,image=TRUE,fista=TRUE,ini=0) |
Details
lasso_multi_back
Value
A list containing:
coefficients: A matrix where each column represents the estimated regression coefficients for a different lambda value.error_evolution: A numeric vector tracking the error at certain step.num_steps: An integer vector indicating the number of steps in which errors are calculated.
Ordinary Least Square regression
Description
This is a function that estimates coefficients for a linear model using Ordinary Least Squares (OLS) regression.
Usage
ols(data,y,x,alpha=0.025,verbose=TRUE)
Arguments
data |
Dataset used to estimated the coefficients |
y |
name of the dependent variable |
x |
name or a vector of names of the independent variables |
alpha |
confedence level |
verbose |
logical, if TRUE, the table will be printed |
Value
coefficients of the linear model, or a table with the coefficients, standard errors, t-values, p-values and confidence intervals
Examples
df = data.frame("hours"=c(1, 2, 4, 5, 5, 6, 6, 7, 8, 10, 11, 11, 12, 12, 14),
"score"=c(64, 66, 76, 73, 74, 81, 83, 82, 80, 88, 84, 82, 91, 93, 89))
ols(df,"score","hours")
K-Fold Cross Validation for OLS
Description
ols_KCV makes the K-Fold Cross Validation for ordinary least squared regression
Usage
ols_KCV(data,k,y,x)
Arguments
data |
full dataset which will be used for KCV |
k |
integer, which indicates how many training and test set will be splited from the dataset |
y |
dependent variable |
x |
independent variables |
Value
the root mean square error after K-Fold Cross Validation on training set
Examples
df<-mtcars
ols_KCV(mtcars,5,"hp",c("mpg","qsec","disp"))
Ridge regression
Description
ridge function estimates the coefficients for a linear model using Ridge regression.
Usage
ridge(data,y,x,lambda)
Arguments
data |
name of the dataset |
y |
name of dependent variables |
x |
name of independent variable |
lambda |
a numeric value or a numeric vector to penalize the squared residual |
Value
a matrix with the coefficients for each lambda
Examples
ridge(mtcars,"hp",c("mpg","qsec","disp"),c(0.01,0.1))
Softmax function for multinomial response variable
Description
the function calculates the softmax function for the multinomial response variable
Usage
softmax(num)
Arguments
num |
A numeric matrix or vector |
Details
softmax
Value
A numeric matrix or vector of the same shape as num, where each element represents a probability value between 0 and 1. The values sum to 1 across each row or the entire vector.