How to create and optimize a baseline Decision Tree model for Regression in R?
This recipe helps you create and optimize a baseline Decision Tree model for Regression in R
Recipe Objective
Decision Tree is a supervised machine learning algorithm which can be used to perform both classification and regression on complex datasets. They are also known as Classification and Regression Trees (CART). Hence, it works for both continuous and categorical variables.
Important basic tree Terminology is as follows:
- Root node: represents an entire popuplation or dataset which gets divided into two or more pure sets (also known as homogeneuos steps). It always contains a single input variable (x).
- Leaf or terminal node: These nodes do not split further and contains the output variable
In this recipe, we will only focus on Regression Trees where the target variable is continuous in nature. The splits in these trees are based on minimising the Residual sum of squares of each groups formed. RSS is calculated by the predicted values is the mean response for the training observations within the jth group.
This recipe demonstrates the modelling and optimisation of a Regression Tree by using the sales data of bags.
STEP 1: Importing Necessary Libraries
library(caret)
library(tidyverse) # for data manipulation
STEP 2: Read a csv file and explore the data
The dataset attached contains the data of 160 different bags associated with ABC industries.
The bags have certain attributes which are described below:
- Height – The height of the bag
- Width – The width of the bag
- Length – The length of the bag
- Weight – The weight the bag can carry
- Weight1 – Weight the bag can carry after expansion
The company now wants to predict the cost they should set for a new variant of these kinds of bags.
data <- read.csv("R_343_Data_1.csv")
glimpse(data)
Rows: 159 Columns: 6 $ Cost242, 290, 340, 363, 430, 450, 500, 390, 450, 500, 475, 500,... $ Weight 23.2, 24.0, 23.9, 26.3, 26.5, 26.8, 26.8, 27.6, 27.6, 28.5,... $ Weight1 25.4, 26.3, 26.5, 29.0, 29.0, 29.7, 29.7, 30.0, 30.0, 30.7,... $ Length 30.0, 31.2, 31.1, 33.5, 34.0, 34.7, 34.5, 35.0, 35.1, 36.2,... $ Height 11.5200, 12.4800, 12.3778, 12.7300, 12.4440, 13.6024, 14.17... $ Width 4.0200, 4.3056, 4.6961, 4.4555, 5.1340, 4.9274, 5.2785, 4.6...
summary(data) # returns the statistical summary of the data columns
Cost Weight Weight1 Length
Min. : 0.0 Min. : 7.50 Min. : 8.40 Min. : 8.80
1st Qu.: 120.0 1st Qu.:19.05 1st Qu.:21.00 1st Qu.:23.15
Median : 273.0 Median :25.20 Median :27.30 Median :29.40
Mean : 398.3 Mean :26.25 Mean :28.42 Mean :31.23
3rd Qu.: 650.0 3rd Qu.:32.70 3rd Qu.:35.50 3rd Qu.:39.65
Max. :1650.0 Max. :59.00 Max. :63.40 Max. :68.00
Height Width
Min. : 1.728 Min. :1.048
1st Qu.: 5.945 1st Qu.:3.386
Median : 7.786 Median :4.248
Mean : 8.971 Mean :4.417
3rd Qu.:12.366 3rd Qu.:5.585
Max. :18.957 Max. :8.142
dim(data)
159 6
STEP 3: Train Test Split
# createDataPartition() function from the caret package to split the original dataset into a training and testing set and split data into training (80%) and testing set (20%)
parts = createDataPartition(data$Cost, p = .8, list = F)
train = data[parts, ]
test = data[-parts, ]
STEP 4: Building and optimising Baseline Regression Tree
We will use caret package to perform Cross Validation and Hyperparameter tuning (max_depth) using grid search technique. First, we will use the trainControl() function to define the method of cross validation to be carried out and search type i.e. "grid" or "random". Then train the model using train() function with tuneGrid as one of the arguements.
Syntax: train(formula, data = , method = , trControl = , tuneGrid = )
where:
- formula = y~x1+x2+x3+..., where y is the independent variable and x1,x2,x3 are the dependent variables
- data = dataframe
- method = Type of the model to be built ("rpart2" for CART)
- trControl = Takes the control parameters. We will use trainControl function out here where we will specify the Cross validation technique.
- tuneGrid = takes the tuning parameters and applies grid search CV on them
# specifying the CV technique which will be passed into the train() function later and number parameter is the "k" in K-fold cross validation
train_control = trainControl(method = "cv", number = 5, search = "grid")
## Customsing the tuning grid (ridge regression has alpha = 0)
Regress_Tree_Grid = expand.grid(maxdepth = c(1,3,5,7,9))
set.seed(50)
# training a Regression model while tuning parameters (Method = "rpart2")
model = train(Cost~., data = train, method = "rpart2", trControl = train_control, tuneGrid = Regress_Tree_Grid)
# summarising the results
print(model)
CART 129 samples 5 predictor No pre-processing Resampling: Cross-Validated (5 fold) Summary of sample sizes: 103, 104, 103, 103, 103 Resampling results across tuning parameters: maxdepth RMSE Rsquared MAE 1 207.8910 0.6593256 157.83357 3 142.9742 0.8496021 103.25668 5 130.2922 0.8751730 87.63598 7 127.8424 0.8794063 85.60232 9 127.8424 0.8794063 85.60232 RMSE was used to select the optimal model using the smallest value. The final value used for the model was maxdepth = 7.
Note: RMSE was used select the optimal model using the smallest value. And the final model has the max depth of 7.
STEP 5: Make predictions on the final Regression Tree model
We use our final Regression Tree model to make predictions on the testing data (unseen data) and predict the 'Cost' value and generate performance measures.
#use model to make predictions on test data
pred_y = predict(model, test)
# performance metrics on the test data
test_y = test[, 1]
mean((test_y - pred_y)^2) #mse - Mean Squared Error
caret::RMSE(test_y, pred_y) #rmse - Root Mean Squared Error
18133.0077888765 134.658857075487
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