diff --git a/M2/Linear Models/Biaised Models/Code_Lec3.Rmd b/M2/Linear Models/Biaised Models/Code_Lec3.Rmd new file mode 100644 index 0000000..eab533d --- /dev/null +++ b/M2/Linear Models/Biaised Models/Code_Lec3.Rmd @@ -0,0 +1,515 @@ +--- +title: "Code: Biased regression" +subtitle: "Methods for Regression and classification" +author: "Katia Meziani" +output: + html_document: + self_contained: true + math_method: + engine: mathjax + url: https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js + code_folding: hide + css: ./style.css + df_print: paged + highlight: tango + number_sections: no + theme: flatly + toc: yes + toc_float: + collapsed: no +--- + + + + + + + + + + + + + + + + + + + + + + + + + +\newcommand{\Lasso}{\widehat{\beta}^{\lambda,L}} +\newcommand{\R}{\mathbb{R}} +\newcommand{\1}{\mathbb{1}} +\newcommand{\RE}{\text{RE}} +\newcommand{\sign}{\text{sign}} +\newcommand{\e}{\epsilon} +\renewcommand{\P}{\text{P}} + +```{r setup, include=FALSE} +knitr::opts_chunk$set(fig.align = "center", message = FALSE, warning = FALSE) +``` + +## Packages + +We begin by loading the necessary packages for this analysis. + +```{r message=FALSE,warning=FALSE} +library(glmnet) # for regularized regression +library(caret) # for training and evaluating models +library(ggplot2) # for data visualization +library(ggfortify) # to extend ggplot2 features for autoplot +library(reshape2) # for reshaping data +library(Metrics) # for calculating metrics like RMSE +library(vip) # for variable importance visualization +library(dplyr) # for data manipulation +library(tidyverse) # includes ggplot2, dplyr, and other useful packages +``` + +**** + +# The Dataset: Cookies + +## Upload Datasets + +```{r} +setwd("/Users/arthurdanjou/Workspace/studies/M2/Linear Models/Biaised Models") +``` + +```{r} +# Loading the training dataset +cookie.train <- read.csv("Cookies_Train.csv", header = TRUE, row.names = 1) +``` + +```{r} +# Loading the test dataset +cookie.test <- read.csv("Cookies_Test.csv", header = TRUE, row.names = 1) +``` + +## Custom Control Parameters + +```{r} +custom <- trainControl( + method = "repeatedcv", + number = 5, # Using 5-fold cross-validation + repeats = 3, # Repeating 3 times for robustness + summaryFunction = defaultSummary, # Default metrics (RMSE, MAE) + allowParallel = TRUE # Use parallel processing if resources allow +) +``` + +**** + +# Models Study + +**** + +## Linear regression analysis + +```{r} +set.seed(602) +linear.mod <- train(sugars ~ ., cookie.train, method = "lm", preProc = c("center", "scale"), trControl = custom) +linear.mod$results +``` + +```{r} +Ytrain <- cookie.train$sugars +dfc_train <- data.frame(ytrain = Ytrain, linear.mod = fitted(linear.mod)) +dfc_train %>% rmarkdown::paged_table() +``` + +```{r} +dfc_train %>% + ggplot(aes(x = ytrain, y = linear.mod)) + + geom_point(size = 2, color = "#983399") + + geom_smooth(method = "lm", color = "#389900") + + ggtitle("Train Dataset") + + ylab("Fitted Values") + + xlab("Actual Values (Y)") +``` + +```{r} +Ytest <- cookie.test$sugars +dfc_test <- data.frame(ytest = Ytest) +dfc_test$linear.mod <- predict(linear.mod, newdata = cookie.test) +# dfc_test%>%rmarkdown::paged_table() + +dfc_test %>% + ggplot(aes(x = ytest, y = linear.mod)) + + geom_point(size = 2, color = "#983399") + + geom_smooth(method = "lm", color = "#389900") + + ggtitle("Test Dataset") + + ylab("Fitted Values") + + xlab("Actual Values (Y)") +``` + +**** + +## Lasso regression analysis + +```{r} +set.seed(602) +# grid_Lasso <- seq(0.001, 0.1, length = 100) +grid_Lasso <- 10^seq(0, 0.1, length = 100) +Lasso <- train(sugars ~ ., cookie.train, + method = "glmnet", + tuneGrid = expand.grid(alpha = 1, lambda = grid_Lasso), + preProc = c("center", "scale"), + trControl = custom +) +``` + +```{r} +library(plotly) +ggplotly(ggplot(Lasso)) +``` + +```{r} +Lasso$results %>% rmarkdown::paged_table() +``` + +```{r} +Lasso$bestTune +``` + +```{r} +Lasso$results[which.min(Lasso$results$RMSE), ] +``` + +```{r} +par(mfrow = c(1, 2)) +plot(Lasso$finalModel, xvar = "lambda", label = TRUE) +plot(Lasso$finalModel, xvar = "dev", label = TRUE) +``` + +```{r} +library(vip) +vip(Lasso, num_features = 15) +``` + +```{r} +coef_lasso <- data.frame( + Variable = rownames(as.matrix(coef(Lasso$finalModel, Lasso$bestTune$lambda))), + Coefficient = as.matrix(coef(Lasso$finalModel, Lasso$bestTune$lambda))[, 1] +) +coef_lasso %>% + subset(Coefficient != 0) %>% + rmarkdown::paged_table() +``` + +**** + +## Ridge regression analysis + +```{r} +set.seed(602) +lambda_ridge <- seq(11, 12, length = 100) +ridge <- train(sugars ~ ., + data = cookie.train, + method = "glmnet", + tuneGrid = expand.grid(alpha = 0, lambda = lambda_ridge), + preProc = c("center", "scale"), + trControl = custom +) +``` + +```{r} +library(plotly) +ggplotly(ggplot(ridge)) +``` + +```{r} +ridge$results %>% rmarkdown::paged_table() +``` + +```{r} +ridge$bestTune +``` + +```{r} +ridge$results[which.min(ridge$results$RMSE), ] +``` + +```{r} +par(mfrow = c(1, 2)) +plot(ridge$finalModel, xvar = "lambda", label = TRUE) +plot(ridge$finalModel, xvar = "dev", label = TRUE) +``` + +```{r} +vip(ridge, num_features = 15) +``` + +```{r} +data.frame(as.matrix(coef(ridge$finalModel, ridge$bestTune$lambda))) %>% + rmarkdown::paged_table() +``` + +**** + +## ElasticNet regression analysis + +```{r} +set.seed(602) +alpha_Enet <- seq(0.5, 0.9, length = 10) +lambda_Enet <- seq(0.01, 0.05, length = 10) + +ElNet <- train(sugars ~ ., cookie.train, + method = "glmnet", + tuneGrid = expand.grid(alpha = alpha_Enet, lambda = lambda_Enet), + preProc = c("center", "scale"), + trControl = custom +) +``` + +```{r} +ggplotly(ggplot(ElNet)) +``` + +```{r} +ElNet$results %>% rmarkdown::paged_table() +``` + +```{r} +ElNet$bestTune +``` + +```{r} +ElNet$results[which.min(ElNet$results$RMSE), ] +``` + +```{r} +par(mfrow = c(1, 2)) +plot(ElNet$finalModel, xvar = "lambda", label = T) +plot(ElNet$finalModel, xvar = "dev", label = T) +``` + +```{r} +vip(ElNet, num_features = 20) +``` + +```{r} +coef_elnet <- data.frame( + Variable = rownames(as.matrix(coef(ElNet$finalModel, ElNet$bestTune$lambda))), + Coefficient = as.matrix(coef(ElNet$finalModel, ElNet$bestTune$lambda))[, 1] +) +coef_elnet %>% + subset(Coefficient != 0) %>% + rmarkdown::paged_table() +``` + +**** + +## PLS regression analysis + +```{r} +set.seed(602) +pls_mod <- train(sugars ~ ., cookie.train, + method = "pls", + tuneLength = 20, + preProc = c("center", "scale"), + trControl = custom +) +``` + +```{r} +ggplotly(ggplot(pls_mod)) +``` + +```{r} +pls_mod$results %>% rmarkdown::paged_table() +``` + +```{r} +pls_mod$bestTune +``` + +```{r} +pls_mod$results[which.min(pls_mod$results$RMSE), ] +``` + +```{r} +vip(pls_mod, num_features = 20) +``` + +```{r} +data.frame(Coefficients = as.matrix(coef(pls_mod$finalModel))) %>% + rmarkdown::paged_table() +``` + +**** + +# Models Comparaison + +**** + +## Graphical comparison of model performance + +### On the training set + +```{r} +yTrain <- cookie.train$sugars +dTrain <- data.frame(yTrain = yTrain) +dTrain$linear <- fitted(linear.mod) +dTrain$Lasso <- fitted(Lasso) +dTrain$ridge <- fitted(ridge) +dTrain$ElNet <- fitted(ElNet) +dTrain$pls <- fitted(pls_mod) +melt.dTrain <- melt(dTrain, id = "yTrain", variable.name = "model") +melt.dTrain %>% ggplot() + + aes(x = yTrain, y = value) + + geom_smooth(method = "lm") + + geom_point(size = 1, colour = "#983399") + + facet_wrap(~model, nrow = 3) + + ggtitle("Train dataset") + + ylab("Fitted value") + + xlab("Y") +``` + +```{r} +dTrain %>% rmarkdown::paged_table() +``` + +```{r} +melt.dTrain %>% rmarkdown::paged_table() +``` + +### On the test set + +```{r} +yTest <- cookie.test$sugars +dTest <- data.frame(yTest = yTest) +dTest$linear <- predict(linear.mod, newdata = cookie.test) +dTest$Lasso <- predict(Lasso, newdata = cookie.test) +dTest$ridge <- predict(ridge, newdata = cookie.test) +dTest$ElNet <- predict(ElNet, newdata = cookie.test) +dTest$pls <- predict(pls_mod, newdata = cookie.test) +# dTest%>% rmarkdown::paged_table() +melt.dTest <- melt(dTest, id = "yTest", variable.name = "model") +# melt.dTest%>% rmarkdown::paged_table() +melt.dTest %>% ggplot() + + aes(x = yTest, y = value) + + geom_smooth(method = "lm") + + geom_point(size = 1, colour = "#983399") + + facet_wrap(~model, nrow = 3) + + ggtitle("Test dataset") + + ylab("Fitted value") + + xlab("Y") + + theme_bw() +``` + +**** + +## RMSE comparaison among models + +```{r} +RMSE <- rbind.data.frame( + cbind(rmse(yTrain, dTrain$linear), rmse(yTest, dTest$linear)), + cbind(rmse(yTrain, dTrain$Lasso), rmse(yTest, dTest$Lasso)), + cbind(rmse(yTrain, dTrain$ridge), rmse(yTest, dTest$ridge)), + cbind(rmse(yTrain, dTrain$ElNet), rmse(yTest, dTest$ElNet)), + cbind(rmse(yTrain, dTrain$pls), rmse(yTest, dTest$pls)) +) +names(RMSE) <- c("Train", "Test") +row.names(RMSE) <- c("Linear", "Lasso", "Ridge", "ElNet", "PLS") +RMSE %>% + kableExtra::kbl() %>% + kableExtra::kable_styling() +``` + +```{r} +summary(yTrain) +summary(yTest) +``` + +```{r, echo=FALSE} +LM_train <- round(rmse(yTrain, dTrain$linear), 2) +LM_test <- round(rmse(yTest, dTest$linear), 2) +Lasso_train <- round(rmse(yTrain, dTrain$Lasso), 2) +Lasso_test <- round(rmse(yTest, dTest$Lasso), 2) +Ridge_train <- round(rmse(yTrain, dTrain$ridge), 2) +Ridge_test <- round(rmse(yTest, dTest$ridge), 2) +ElNet_train <- round(rmse(yTrain, dTrain$ElNet), 2) +ElNet_test <- round(rmse(yTest, dTest$ElNet), 2) +PLS_train <- round(rmse(yTrain, dTrain$pls), 2) +PLS_test <- round(rmse(yTest, dTest$pls), 2) +``` \ No newline at end of file diff --git a/M2/Linear Models/Biaised Models/Code_Lec3.html b/M2/Linear Models/Biaised Models/Code_Lec3.html new file mode 100644 index 0000000..8094372 --- /dev/null +++ b/M2/Linear Models/Biaised Models/Code_Lec3.html @@ -0,0 +1,5696 @@ + + + + + + + + + + + + + + +Code: Biased regression + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + +
+
+
+
+
+ +
+ + + + + + + + + + + + + + + + + + + +
+

Packages

+

We begin by loading the necessary packages for this analysis.

+
library(glmnet)    # for regularized regression
+library(caret)      # for training and evaluating models
+library(ggplot2)    # for data visualization
+library(ggfortify)  # to extend ggplot2 features for autoplot
+library(reshape2)   # for reshaping data
+library(Metrics)    # for calculating metrics like RMSE
+library(vip)        # for variable importance visualization
+library(dplyr)      # for data manipulation
+library(tidyverse)  # includes ggplot2, dplyr, and other useful packages
+
+
+
+

The Dataset: Cookies

+
+

Upload Datasets

+
# Loading the training dataset
+cookie.train <- read.csv('Cookies_Train.csv', header = TRUE, row.names = 1)
+
# Loading the test dataset
+cookie.test <- read.csv('Cookies_Test.csv', header = TRUE, row.names = 1)
+
+
+

Custom Control Parameters

+
custom <- trainControl(
+  method = 'repeatedcv',
+  number = 5,  # Using 5-fold cross-validation
+  repeats = 3,  # Repeating 3 times for robustness
+  summaryFunction = defaultSummary,  # Default metrics (RMSE, MAE)
+  allowParallel = TRUE  # Use parallel processing if resources allow
+)
+
+
+
+
+

Models Study

+
+
+

Linear regression analysis

+
set.seed(602)
+linear.mod <- train(sugars~.,cookie.train,
+                  method='lm',
+                  preProc = c("center", "scale"),
+                  trControl=custom)
+linear.mod$results
+
+ +
+
Ytrain <- cookie.train$sugars
+dfc_train <- data.frame(ytrain=Ytrain, linear.mod = fitted(linear.mod))
+dfc_train %>% rmarkdown::paged_table()
+
+ +
+
dfc_train %>% 
+  ggplot(aes(x = ytrain, y = linear.mod)) + 
+  geom_point(size = 2, color = "#983399") +
+  geom_smooth(method = "lm", color = "#389900") +
+  ggtitle("Train Dataset") +
+  ylab("Fitted Values") + 
+  xlab("Actual Values (Y)")
+

+
Ytest<-cookie.test$sugars
+dfc_test<-data.frame(ytest=Ytest)
+dfc_test$linear.mod<-predict(linear.mod,newdata = cookie.test)
+#dfc_test%>%rmarkdown::paged_table()
+
+dfc_test %>% 
+  ggplot(aes(x = ytest, y = linear.mod)) + 
+  geom_point(size = 2, color = "#983399") +
+  geom_smooth(method = "lm", color = "#389900") +
+  ggtitle("Test Dataset") +
+  ylab("Fitted Values") + 
+  xlab("Actual Values (Y)")
+

+
+
+
+

Lasso regression analysis

+
set.seed(602)
+#grid_Lasso <- seq(0.001, 0.1, length = 100)
+grid_Lasso <- 10^seq(-4, -1, length = 100) 
+Lasso <- train(sugars ~ ., cookie.train,
+               method = 'glmnet',
+               tuneGrid = expand.grid(alpha = 1, lambda = grid_Lasso),
+               preProc = c("center", "scale"),
+               trControl = custom)
+
library(plotly)
+ggplotly(ggplot(Lasso))
+
+ +
Lasso$results%>%rmarkdown::paged_table()
+
+ +
+
Lasso$bestTune
+
+ +
+
Lasso$results[which.min(Lasso$results$RMSE), ]
+
+ +
+
par(mfrow=c(1, 2))
+plot(Lasso$finalModel, xvar = "lambda", label = TRUE)
+plot(Lasso$finalModel, xvar = "dev", label = TRUE)
+

+
library(vip)    
+vip(Lasso,num_features = 15)
+

+
coef_lasso <- data.frame(
+  Variable = rownames(as.matrix(coef(Lasso$finalModel, Lasso$bestTune$lambda))),
+  Coefficient = as.matrix(coef(Lasso$finalModel, Lasso$bestTune$lambda))[,1]
+)
+coef_lasso %>% subset(Coefficient != 0) %>% rmarkdown::paged_table()
+
+ +
+
+
+
+

Ridge regression analysis

+
set.seed(602)
+lambda_ridge <- seq(11, 12, length = 100)
+ridge <- train(sugars ~ ., data = cookie.train,
+               method = 'glmnet',
+               tuneGrid = expand.grid(alpha = 0, lambda = lambda_ridge),
+               preProc = c("center", "scale"),
+               trControl = custom
+               )
+
library(plotly)
+ggplotly(ggplot(ridge))
+
+ +
ridge$results%>%rmarkdown::paged_table()
+
+ +
+
ridge$bestTune
+
+ +
+
ridge$results[which.min(ridge$results$RMSE), ]
+
+ +
+
par(mfrow=c(1, 2))
+plot(ridge$finalModel, xvar = "lambda", label = TRUE)
+plot(ridge$finalModel, xvar = "dev", label = TRUE)
+

+
vip(ridge,num_features = 15)
+

+
data.frame(as.matrix(coef(ridge$finalModel, ridge$bestTune$lambda))) %>%
+  rmarkdown::paged_table()
+
+ +
+
+
+
+

ElasticNet regression analysis

+
set.seed(602)
+alpha_Enet <- seq(0.5, 0.9, length = 10)
+lambda_Enet <- seq(0.01, 0.05, length = 10)
+
+ElNet <- train(sugars ~ ., cookie.train,
+               method = 'glmnet',
+               tuneGrid = expand.grid(alpha = alpha_Enet, lambda = lambda_Enet),
+               preProc = c("center", "scale"),
+               trControl = custom)
+
ggplotly(ggplot(ElNet))
+
+ +
ElNet$results%>%rmarkdown::paged_table()
+
+ +
+
ElNet$bestTune
+
+ +
+
ElNet$results[which.min(ElNet$results$RMSE), ]
+
+ +
+
par(mfrow=c(1, 2))
+plot(ElNet$finalModel,xvar="lambda",label=T)
+plot(ElNet$finalModel,xvar="dev",label=T)
+

+
vip(ElNet,num_features = 20)
+

+
coef_elnet <- data.frame(
+  Variable = rownames(as.matrix(coef(ElNet$finalModel, ElNet$bestTune$lambda))),
+  Coefficient = as.matrix(coef(ElNet$finalModel, ElNet$bestTune$lambda))[,1]
+)
+coef_elnet %>% subset(Coefficient != 0) %>% rmarkdown::paged_table()
+
+ +
+
+
+
+

PLS regression analysis

+
set.seed(602)
+pls_mod <- train(sugars ~ ., cookie.train,
+                 method = 'pls',
+                 tuneLength = 20,
+                 preProc = c("center", "scale"),
+                 trControl = custom)
+
ggplotly(ggplot(pls_mod))
+
+ +
pls_mod$results%>%rmarkdown::paged_table()
+
+ +
+
pls_mod$bestTune
+
+ +
+
pls_mod$results[which.min(pls_mod$results$RMSE), ]
+
+ +
+
vip(pls_mod,num_features = 20)
+

+
data.frame(Coefficients = as.matrix(coef(pls_mod$finalModel))) %>% rmarkdown::paged_table()
+
+ +
+
+
+
+
+

Models Comparaison

+
+
+

Graphical comparison of model performance

+
+

On the training set

+
yTrain<-cookie.train$sugars 
+dTrain<-data.frame(yTrain=yTrain) 
+dTrain$linear<-fitted(linear.mod)
+dTrain$Lasso<-fitted(Lasso)
+dTrain$ridge<-fitted(ridge)
+dTrain$ElNet<-fitted(ElNet)
+dTrain$pls<-fitted(pls_mod)
+melt.dTrain<-melt(dTrain,id="yTrain",variable.name="model")
+melt.dTrain%>%ggplot()+aes(x = yTrain, y = value)+geom_smooth(method = "lm")+ geom_point(size=1, colour="#983399")+ facet_wrap( ~ model,nrow=3) + ggtitle("Train dataset")+
+  ylab("Fitted value") + xlab(" Y ")
+

+
dTrain%>% rmarkdown::paged_table()
+
+ +
+
melt.dTrain%>% rmarkdown::paged_table()
+
+ +
+
+
+

On the test set

+
yTest<-cookie.test$sugars
+dTest<-data.frame(yTest=yTest)
+dTest$linear<-predict(linear.mod, newdata = cookie.test) 
+dTest$Lasso<-predict(Lasso, newdata = cookie.test) 
+dTest$ridge<-predict(ridge, newdata = cookie.test) 
+dTest$ElNet<-predict(ElNet, newdata = cookie.test) 
+dTest$pls<- predict(pls_mod, newdata = cookie.test)
+#dTest%>% rmarkdown::paged_table()
+melt.dTest<-melt(dTest,id="yTest",variable.name="model")
+#melt.dTest%>% rmarkdown::paged_table()
+melt.dTest%>%ggplot()+aes(x = yTest, y = value)+geom_smooth(method = "lm")+ geom_point(size=1, colour="#983399")+ facet_wrap( ~ model,nrow=3) + ggtitle("Test dataset")+
+  ylab("Fitted value") + xlab(" Y ") + theme_bw()
+

+
+
+
+
+

RMSE comparaison among models

+
RMSE<-rbind.data.frame(
+cbind(rmse(yTrain,dTrain$linear),rmse(yTest,dTest$linear)),
+cbind(rmse(yTrain,dTrain$Lasso),rmse(yTest,dTest$Lasso )),
+cbind(rmse(yTrain,dTrain$ridge),rmse(yTest,dTest$ridge )),
+cbind(rmse(yTrain,dTrain$ElNet),rmse(yTest,dTest$ElNet)),
+cbind(rmse(yTrain,dTrain$pls),rmse(yTest,dTest$pls )))
+names(RMSE)=c("Train","Test")
+row.names(RMSE)=c("Linear","Lasso","Ridge","ElNet","PLS")
+RMSE%>% kableExtra::kbl() %>% kableExtra::kable_styling()
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +Train + +Test +
+Linear + +0.000000 + +11.598358 +
+Lasso + +1.125158 + +1.060734 +
+Ridge + +2.526064 + +2.594585 +
+ElNet + +1.133296 + +1.095012 +
+PLS + +2.271071 + +1.306989 +
+
summary(yTrain)
+
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
+##    9.95   13.32   16.36   16.54   19.82   23.11
+
summary(yTest)
+
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
+##   10.12   13.38   16.66   16.66   19.93   23.19
+
+
+ + + +
+
+ +
+ + + + + + + + + + + + + + + + + diff --git a/M2/Linear Models/Biaised Models/Cookies_Test.csv b/M2/Linear Models/Biaised Models/Cookies_Test.csv new file mode 100644 index 0000000..5510122 --- /dev/null +++ b/M2/Linear Models/Biaised Models/Cookies_Test.csv @@ -0,0 +1,33 @@ 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