Iris using Naive Bayes

library(tidyverse)
library(e1071)

• Use naiveBayes to classify the iris flowers into their three classes.

nb_iris <- naiveBayes(Species ~ ., data = iris)

• What information does the $tables from the fit contain?

nb_iris$tables %>% lapply(function(x){
  colnames(x) <- c("mean", "sd")
  x
})

$Sepal.Length
            Sepal.Length
Y             mean        sd
  setosa     5.006 0.3524897
  versicolor 5.936 0.5161711
  virginica  6.588 0.6358796

$Sepal.Width
            Sepal.Width
Y             mean        sd
  setosa     3.428 0.3790644
  versicolor 2.770 0.3137983
  virginica  2.974 0.3224966

$Petal.Length
            Petal.Length
Y             mean        sd
  setosa     1.462 0.1736640
  versicolor 4.260 0.4699110
  virginica  5.552 0.5518947

$Petal.Width
            Petal.Width
Y             mean        sd
  setosa     0.246 0.1053856
  versicolor 1.326 0.1977527
  virginica  2.026 0.2746501

• Try to identify the most informative variables for predicting the classes.

pars_iris <- nb_iris$tables %>% 
  lapply(function(x){
  x %>% as.data.frame() %>% 
    mutate(Species = rownames(.)) %>% 
    set_names(c("mean", "sd", "species"))
    }) %>% 
  bind_rows(.id = "variable")
pars_iris_ <- pars_iris %>% 
  mutate(x = list(seq(0, 12, len = 100))) %>% 
  unnest() %>% 
  mutate(d_x = dnorm(x = x, mean = mean , sd = sd))

ggplot(pars_iris_, aes(x = x, y = d_x, colour = species)) + 
  facet_wrap(~variable, scales = "free_y") + geom_line()

• Are the assumptions about normality satisfied for each of \(x_i\mid y\)?

qq_iris <- function(column){
  par(mfrow = c(1,3))
  for(i in unique(iris$Species)){
    ii <- iris %>% filter(Species == i) %>% pull(column)
    qqnorm(ii, main = i)
    mtext(side = 3, line = 0.7, column, cex = 0.8)
    qqline(ii)
    }
}
qq_iris("Petal.Length")

qq_iris("Petal.Width")

qq_iris("Sepal.Length")
qq_iris("Sepal.Length")

• Can you visualise the decision boundaries in the Petal-plane (i.e x = Petal.Length, y = Petal.Width)? Tip:* Create a grid (cf below), make the prediction for each* point in the grid and plot this.

iris_petal_grid <- iris %>% 
  expand(
    Petal.Length = seq(min(Petal.Length), max(Petal.Length), len = 100),
    Petal.Width = seq(min(Petal.Width), max(Petal.Width), len = 100)
  ) %>% 
  mutate(Sepal.Length = NA, Sepal.Width = NA)

iris_nb <- naiveBayes(Species ~ ., data = iris)
iris_petal_grid$pred <- predict(iris_nb, newdata = iris_petal_grid)
iris_petal_grid %>% 
  ggplot(aes(x = Petal.Length, y = Petal.Width, colour = pred)) + geom_point(alpha = 0.5) +
  geom_point(data = iris, aes(fill = Species, colour = NULL), pch = 21, colour = "black")