In this practical, we will focus on two different classification methods: K-nearest neighbours and logistic regression.
One of the packages we are going to use is class
. For this, you will probably need to install.packages("class")
before running the library()
functions. ISLR
is also a new package, that needs to be installed to access the Default
data.
library(MASS)
library(magrittr)
library(class)
library(ISLR)
library(tidyverse)
library(caret)
Before starting with the exercises, it is a good idea to set your seed, so that (1) your answers are reproducible and (2) you can compare your answers with the answers provided.
set.seed(45)
ISLR
The default dataset contains credit card loan data for 10 000 people. The goal is to classify credit card cases as yes
or no
based on whether they will default on their loan.
Default
dataset, where balance
is mapped to the x position, income
is mapped to the y position, and default
is mapped to the colour. Can you see any interesting patterns already?+ facet_grid(cols = vars(student))
to the plot. What do you see?ifelse()
(0 = not a student, 1 = student). Then, randomly split the Default dataset into a training set train
(80%) and a test set test
(20%).Now that we have explored the dataset, we can start on the task of classification. We can imagine a credit card company wanting to predict whether a customer will default on the loan so they can take steps to prevent this from happening.
The first method we will be using is k-nearest neighbours (KNN). It classifies datapoints based on a majority vote of the k points closest to it. In R
, the class
package contains a knn()
function to perform knn.
knn()
function. Use student
, balance
, and income
(but no basis functions of those variables) in the train
dataset. Set k
to 5. Store the predictions in a variable called knn_5_pred
.default
) mapped to the colour aesthetic, and one with the predicted class (knn_5_pred
) mapped to the colour aesthetic.Hint: Add the predicted class knn_5_pred
to the test
dataset before starting your ggplot()
call of the second plot. What do you see?
knn_2_pred
vector generated from a 2-nearest neighbours algorithm. Are there any differences?The confusion matrix is an insightful summary of the plots we have made and the correct and incorrect classifications therein. A confusion matrix can be made in R
with the confusionMatrix()
function from the caret
package.
confusionMatrix(knn_2_pred, test$default)
KNN directly predicts the class of a new observation using a majority vote of the existing observations closest to it. In contrast to this, logistic regression predicts the log-odds
of belonging to category 1. These log-odds can then be transformed to probabilities by performing an inverse logit transform:
\[ p = \frac{1}{1+e^{-\alpha}},\] where \(\alpha\) indicates log-odds for being in class 1 and \(p\) is the probability.
Therefore, logistic regression is a probabilistic
classifier as opposed to a direct
classifier such as KNN: indirectly, it outputs a probability which can then be used in conjunction with a cutoff (usually 0.5) to classify new observations.
Logistic regression in R
happens with the glm()
function, which stands for generalized linear model. Here we have to indicate that the residuals are modeled not as a gaussian (normal distribution), but as a binomial
distribution.
glm()
with argument family = binomial
to fit a logistic regression model fit
to the train
data.fit
. You can choose for yourself which type of visualisation you would like to make. Write down your interpretations along with your plot.fit
model and interpret the coefficient for balance
. What would the probability of default be for a person who is not a student, has an income of 40000, and a balance of 3000 dollars at the end of each month? Is this what you expect based on the plots we’ve made before?In two steps, we will visualise the effect balance
has on the predicted default probability.
balance_df
with 3 columns and 500 rows: student
always 0, balance
ranging from 0 to 3000, and income
always the mean income in the train
dataset.newdata
in a predict()
call using fit
to output the predicted probabilities for different values of balance
. Then create a plot with the balance_df$balance
variable mapped to x and the predicted probabilities mapped to y. Is this in line with what you expect?End of Practical