Add initial R project configuration file (studies.Rproj) with default settings

M2/Linear Models/Biaised Models/Code_Lec3.Rmd

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+---
+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
+---
+
+<style>
+.column {
+  width: 50%;
+  float: left;
+}
+</style>
+
+<style>
+.image-wrapper {
+  text-align: center; /* Centre toutes les images */
+}
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+  display: inline-block;
+  margin-right: 20px; /* Espacement entre les images */
+  text-align: center;  /* Centre le texte sous l'image */
+}
+.image-container:last-child {
+  margin-right: 0; /* Pas d'espacement après la dernière image */
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+</style>
+
+<style>
+.attention {
+  font-size: 24px;
+  color: red;
+  font-weight: bold;
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+.underline {
+  text-decoration: underline;
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+  border: 2px solid black; ; padding: 5px
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+  border: 2px solid black; 
+  padding: 10px; /* Espace interne */
+  background-color: rgba(128, 0, 128, 0.05); /* Fond violet très très clair avec transparence */
+  margin: 10px 0; /* Espace autour de l'encadrement */
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+.brdred {
+  border: 2px solid #B22222 ; 
+  padding: 10px; /* Ajouter de l'espace autour du texte */
+  background-color: #f9f9f9; /* Optionnel : couleur de fond pour le texte */
+  margin: 10px 0; /* Ajouter de l'espace au-dessus et en-dessous de l'encadrement */
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+</style>
+
+<style>
+.solution {
+  font-size: 24px;
+  color: yellow; /* Couleur jaune pour simuler la lumière */
+}
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+.underline {
+  text-decoration: underline;
+}
+</style>
+
+<style>
+.brdgreen {
+  border: 2px solid black; /* Bordure verte */
+  padding: 10px; /* Espace interne */
+  background-color: rgba(114, 213, 114, 0.03); /* Fond vert pastel très clair avec transparence */
+  margin: 10px 0; /* Espace autour de l'encadrement */
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+</style>
+
+<style>
+.brdblack {
+  border: 2px solid black; /* Définir la couleur et l'épaisseur de la bordure */
+  padding: 10px; /* Ajouter de l'espace autour du texte */
+  background-color: #f9f9f9; /* Optionnel : couleur de fond pour le texte */
+  margin: 10px 0; /* Ajouter de l'espace au-dessus et en-dessous de l'encadrement */
+}
+</style>
+
+<style>
+.brdblackempty {
+  border: 2px solid black; /* Définir la couleur et l'épaisseur de la bordure */
+  padding: 10px; /* Ajouter de l'espace autour du texte */
+  margin: 10px 0; /* Ajouter de l'espace au-dessus et en-dessous de l'encadrement */
+}
+</style>
+
+\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)
+```

studies.Rproj

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+Version: 1.0
+
+RestoreWorkspace: Default
+SaveWorkspace: Default
+AlwaysSaveHistory: Default
+
+EnableCodeIndexing: Yes
+UseSpacesForTab: Yes
+NumSpacesForTab: 2
+Encoding: UTF-8
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+RnwWeave: Sweave
+LaTeX: pdfLaTeX