K-fold Cross Validation in R Programming

The prime aim of any machine learning model is to predict the outcome of real-time data. To check whether the developed model is efficient enough to predict the outcome of an unseen data point, performance evaluation of the applied machine learning model becomes very necessary. K-fold cross-validation technique is basically a method of resampling the data set in order to evaluate a machine learning model. In this technique, the parameter K refers to the number of different subsets that the given data set is to be split into. Further, K-1 subsets are used to train the model and the left out subsets are used as a validation set.

Steps involved in the K-fold Cross Validation in R: 

1. Split the data set into K subsets randomly
2. For each one of the developed subsets of data points
   • Treat that subset as the validation set
   • Use all the rest subsets for training purpose
   • Training of the model and evaluate it on the validation set or test set
   • Calculate prediction error
3. Repeat the above step K times i.e., until the model is not trained and tested on all subsets
4. Generate overall prediction error by taking the average of prediction errors in every case

To implement all the steps involved in the K-fold method, the R language has rich libraries and packages of inbuilt functions through which it becomes very easy to carry out the complete task. The following are the step-by-step procedure to implement the K-fold technique as a cross-validation method on Classification and Regression machine learning models.

Implement the K-fold Technique on Classification

Classification machine learning models are preferred when the target variable consist of categorical values like spam, not spam, true or false, etc. Here Naive Bayes classifier will be used as a probabilistic classifier to predict the class label of the target variable.  

Step 1:  Loading the dataset and other required packages

The very first requirement is to set up the R environment by loading all required libraries as well as packages to carry out the complete process without any failure. Below is the implementation of this step.

R

# loading required packages

# package to perform data manipulation
# and visualization
library(tidyverse)

# package to compute
# cross - validation methods
library(caret)

# loading package to
# import desired dataset
library(ISLR)

 Step 2: Exploring the dataset

In order to perform manipulations on the data set, it is very necessary to inspect it first. It will give a clear idea about the structure as well as the various kinds of data types present in the data set. For this purpose, the data set must be assigned to a variable. Below is the code to do the same.

R

# assigning the complete dataset
# Smarket to a variable
dataset <- Smarket[complete.cases(Smarket), ]

# display the dataset with details
# like column name and its data type
# along with values in each row
glimpse(dataset)

# checking values present
# in the Direction column
# of the dataset
table(dataset$Direction)

Output:

Rows: 1,250

Columns: 9

$ Year      <dbl> 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, …

$ Lag1      <dbl> 0.381, 0.959, 1.032, -0.623, 0.614, 0.213, 1.392, -0.403, 0.027, 1.303, 0.287, -0.498, -0.189, 0.680, 0.701, -0.562, 0.546, -1…

$ Lag2      <dbl> -0.192, 0.381, 0.959, 1.032, -0.623, 0.614, 0.213, 1.392, -0.403, 0.027, 1.303, 0.287, -0.498, -0.189, 0.680, 0.701, -0.562, 0…

$ Lag3      <dbl> -2.624, -0.192, 0.381, 0.959, 1.032, -0.623, 0.614, 0.213, 1.392, -0.403, 0.027, 1.303, 0.287, -0.498, -0.189, 0.680, 0.701, -…

$ Lag4      <dbl> -1.055, -2.624, -0.192, 0.381, 0.959, 1.032, -0.623, 0.614, 0.213, 1.392, -0.403, 0.027, 1.303, 0.287, -0.498, -0.189, 0.680, …

$ Lag5      <dbl> 5.010, -1.055, -2.624, -0.192, 0.381, 0.959, 1.032, -0.623, 0.614, 0.213, 1.392, -0.403, 0.027, 1.303, 0.287, -0.498, -0.189, …

$ Volume    <dbl> 1.19130, 1.29650, 1.41120, 1.27600, 1.20570, 1.34910, 1.44500, 1.40780, 1.16400, 1.23260, 1.30900, 1.25800, 1.09800, 1.05310, …

$ Today     <dbl> 0.959, 1.032, -0.623, 0.614, 0.213, 1.392, -0.403, 0.027, 1.303, 0.287, -0.498, -0.189, 0.680, 0.701, -0.562, 0.546, -1.747, 0…

$ Direction <fct> Up, Up, Down, Up, Up, Up, Down, Up, Up, Up, Down, Down, Up, Up, Down, Up, Down, Up, Down, Down, Down, Down, Up, Down, Down, Up…

> table(dataset$Direction)

Down   Up 

 602  648 

According to the above information, the dataset contains 250 rows and 9 columns. The data type of independent variables is <dbl> which comes from double and it means the double-precision floating-point number. The target variable is of <fct> data type means factor and it is desirable for a classification model. Moreover, the target variable has 2 outcomes, namely Down and Up where the ratio of these two categories is almost 1:1, i.e., they are balanced. All the categories of the target variable must be in approximately equal proportion to make an unbiased model. 

For this purpose, there are many techniques like:

• Down Sampling
• Up Sampling
• Hybrid Sampling using SMOTE and ROSE

Step 3: Building the model with K-fold algorithm

In this step, the trainControl() function is defined to set the value of the K parameter and then the model is developed as per the steps involved in the K-fold technique. Below is the implementation. 

R

# setting seed to generate a
# reproducible random sampling
set.seed(123)

# define training control which
# generates parameters that further
# control how models are created
train_control <- trainControl(method = "cv",
                              number = 10)


# building the model and
# predicting the target variable
# as per the Naive Bayes classifier
model <- train(Direction~., data = dataset,
               trControl = train_control,
               method = "nb")

Step 4:  Evaluating the accuracy of the model

After training and validation of the model, it is time to calculate the overall accuracy of the model. Below is the code to generate a summary of the model. 

R

# summarize results of the
# model after calculating
# prediction error in each case
print(model)

Output:

Naive Bayes 

1250 samples

   8 predictor

   2 classes: ‘Down’, ‘Up’ 

No pre-processing

Resampling: Cross-Validated (10 fold) 

Summary of sample sizes: 1125, 1125, 1125, 1126, 1125, 1124, … 

Resampling results across tuning parameters:

  usekernel  Accuracy   Kappa    

  FALSE      0.9543996  0.9083514

   TRUE      0.9711870  0.9422498

Tuning parameter ‘fL’ was held constant at a value of 0

Tuning parameter ‘adjust’ was held constant at a value of 1

Accuracy was used to select the optimal model using the largest value.

The final values used for the model were fL = 0, usekernel = TRUE and adjust = 1.

Implement the K-fold Technique on Regression

Regression machine learning models are used to predict the target variable which is of continuous nature like the price of a commodity or sales of a firm. Below are the complete steps for implementing the K-fold cross-validation technique on regression models.

Step 1: Importing all required packages

Set up the R environment by importing all necessary packages and libraries. Below is the implementation of this step. 

R

# loading required packages

# package to perform data manipulation
# and visualization
library(tidyverse)

# package to compute
# cross - validation methods
library(caret)

# installing package to
# import desired dataset
install.packages("datarium")

Step 2: Loading and inspecting the dataset

In this step, the desired dataset is loaded in the R environment. After that, some rows of the data set are printed in order to understand its structure. Below is the code to carry out this task.

R

# loading the dataset
data("marketing", package = "datarium")

# inspecting the dataset
head(marketing)

Output:

  youtube facebook newspaper sales
1  276.12    45.36     83.04 26.52
2   53.40    47.16     54.12 12.48
3   20.64    55.08     83.16 11.16
4  181.80    49.56     70.20 22.20
5  216.96    12.96     70.08 15.48
6   10.44    58.68     90.00  8.64

Step 3: Building the model with K-fold algorithm

The value of the K parameter is defined in the trainControl() function and the model is developed according to the steps mentioned in the algorithm of the K-fold cross-validation technique. Below is the implementation. 

R

# setting seed to generate a
# reproducible random sampling
set.seed(125)

# defining training control
# as cross-validation and
# value of K equal to 10
train_control <- trainControl(method = "cv",
                              number = 10)

# training the model by assigning sales column
# as target variable and rest other column
# as independent variable
model <- train(sales ~., data = marketing,
               method = "lm",
               trControl = train_control)

Step 4: Evaluate the model performance

As mentioned in the algorithm of K-fold that model is tested against every unique fold(or subset) of the dataset and in each case, the prediction error is calculated and at last, the mean of all prediction errors is treated as the final performance score of the model. So, below is the code to print the final score and overall summary of the model. 

R

# printing model performance metrics
# along with other details
print(model)

Output:

Linear Regression 

200 samples

  3 predictor

No pre-processing

Resampling: Cross-Validated (10 fold) 

Summary of sample sizes: 181, 180, 180, 179, 180, 180, … 

Resampling results:

  RMSE      Rsquared   MAE     

  2.027409  0.9041909  1.539866

Tuning parameter ‘intercept’ was held constant at a value of TRUE

Advantages of K-fold Cross-Validation

• Fast computation speed.
• A very effective method to estimate the prediction error and the accuracy of a model.

Disadvantages of K-fold Cross-Validation

• A lower value of K leads to a biased model and a higher value of K can lead to variability in the performance metrics of the model. Thus, it is very important to use the correct value of K for the model (generally K = 5 and K = 10 is desirable).