```{r}
library(randomForest)
library(MASS)
library(tree)
data(Boston)
```

## Sampling

```{r}
set.seed(123)
appr <- sample(seq_len(nrow(Boston)), nrow(Boston) / 2)
```

## Regression Tree

```{r}
arbre_boston <- tree(medv ~ ., Boston, subset = appr)
summary(arbre_boston)
plot(arbre_boston)
text(arbre_boston, pretty = 0)
```


```{r}
cv_boston <- cv.tree(arbre_boston)
plot(cv_boston$size, cv_boston$dev, type = "b")
```


```{r}
yprev <- predict(arbre_boston, newdata = Boston[-appr, ])
boston_test <- Boston[-appr, "medv"]
plot(yprev, boston_test)
abline(0, 1)
mean((yprev - boston_test)^2)
```

## Bagging

```{r}
set.seed(123)

bag_boston <- randomForest(
  medv ~ .,
  data = Boston,
  subset = appr,
  mtry = 13,
  importance = TRUE
)
bag_boston
yprev_bag <- predict(bag_boston, newdata = Boston[-appr, ])
plot(yprev_bag, boston_test)
abline(0, 1)
mean((yprev_bag - boston_test)^2)
```

## Random Forest

```{r}
set.seed(123)
rf_boston <- randomForest(
  medv ~ .,
  data = Boston,
  subset = appr,
  mtry = 6,
  importance = TRUE
)
yprev_rf <- predict(rf_boston, newdata = Boston[-appr, ])
mean((yprev_rf - boston_test)^2)
```

## Variable importance

```{r}
importance(rf_boston)
varImpPlot(rf_boston)
```

# Boosting

```{r}
library(gbm)
set.seed(1)
boost_boston <- gbm(
  medv ~ .,
  data = Boston[appr, ],
  distribution = "gaussian",
  n.trees = 5000,
  interaction.depth = 4
)

summary(boost_boston)

par(mfrow = c(1, 2))
plot(boost_boston, i = "rm")
plot(boost_boston, i = "lstat")
```

```{r}
yhat_boost <- predict(boost_boston, newdata = Boston[-appr, ], n.trees = 5000)
mean((yhat_boost - boston_test)^2)
```

```{r}
boost_boston <- gbm(
  medv ~ .,
  data = Boston[appr, ],
  distribution = "gaussian",
  n.trees = 5000,
  interaction.depth = 4,
  shrinkage = 0.2,
  verbose = FALSE
)

yhat_boost <- predict(boost_boston, newdata = Boston[-appr, ], n.trees = 5000)
mean((yhat_boost - boston_test)^2)
```