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CART (Classification And Regression Tree) in Machine Learning

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  • Last Updated : 23 Sep, 2022
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CART( Classification And Regression Tree) is a  variation of the decision tree algorithm. It can handle both classification and regression tasks. Scikit-Learn uses the Classification And Regression Tree (CART) algorithm to train  Decision Trees (also called “growing” trees). CART was first produced by Leo Breiman, Jerome Friedman, Richard Olshen, and Charles Stone in 1984.

CART Algorithm

CART is a predictive algorithm used in Machine learning and it explains how the target variable’s values can be predicted based on other matters. It is a decision tree where each fork is split into a predictor variable and each node has a prediction for the target variable at the end.

In the decision tree, nodes are split into sub-nodes on the basis of a threshold value of an attribute. The root node is taken as the training set and is split into two by considering the best attribute and threshold value. Further, the subsets are also split using the same logic. This continues till the last pure sub-set is found in the tree or the maximum number of leaves possible in that growing tree.

The CART algorithm works via the following process:

  • The best split point of each input is obtained. 
  • Based on the best split points of each input in Step 1, the new “best” split point is identified. 
  • Split the chosen input according to the “best” split point. 
  • Continue splitting until a stopping rule is satisfied or no further desirable splitting is available.


CART algorithm uses Gini Impurity to split the dataset into a decision tree .It does that by searching for the best homogeneity for the sub nodes, with the help of the Gini index criterion.

Gini index/Gini impurity

The Gini index is a metric for the classification tasks in CART. It stores the sum of squared probabilities of each class. It computes the degree of probability of a specific variable that is wrongly being classified when chosen randomly and a variation of the Gini coefficient. It works on categorical variables, provides outcomes either “successful” or “failure” and hence conducts binary splitting only.

The degree of the  Gini index varies from 0 to 1,

  • Where 0 depicts that all the elements are allied to a certain class, or only one class exists there.
  • The Gini index of value 1 signifies that all the elements are randomly distributed across various classes, and
  • A value of 0.5 denotes the elements are uniformly distributed into some classes.

Mathematically, we can write Gini Impurity as follows: 

Gini = 1 -\sum_{i=1}^{n} (pi)^{{2}}

where pi is the probability of an object being classified to a particular class.

Classification tree

A classification tree is an algorithm where the target variable is categorical. The algorithm is then used to identify the “Class” within which the target variable is most likely to fall. Classification trees are used when the dataset needs to be split into classes that belong to the response variable(like yes or no)

Regression tree

A Regression tree is an algorithm where the target variable is continuous and the tree is used to predict its value. Regression trees are used when the response variable is continuous. For example, if the response variable is the temperature of the day.

Pseudo-code of the CART algorithm

d = 0, endtree = 0
Note(0) = 1, Node(1) = 0, Node(2) = 0
while endtree < 1
    if Node(2d-1) + Node(2d) + .... + Node(2d+1-2) = 2 - 2d+1   
        endtree = 1
        do i = 2d-1, 2d, .... , 2d+1-2
            if Node(i) > -1
                Split tree
                Node(2i+1) = -1
                Node(2i+2) = -1
            end if
        end do
    end if
d = d + 1
end while

CART model representation

CART models are formed by picking input variables and evaluating split points on those variables until an appropriate tree is produced.

Steps to create a Decision Tree using the  CART algorithm:

  • Greedy algorithm: In this The input space is divided using the  Greedy method which is known as a recursive binary spitting.  This is a numerical method within which all of the values are aligned and several other split points are tried and assessed using a cost function.
  • Stopping Criterion: As it works its way down the tree with the training data, the recursive binary splitting method described above must know when to stop splitting. The most frequent halting method is to utilize a minimum amount of training data allocated to every leaf node. If the count is smaller than the specified threshold, the split is rejected and also the node is considered the last leaf node.
  • Tree pruning: Decision tree’s complexity is defined as the number of splits in the tree. Trees with fewer branches are recommended as they are simple to grasp and less prone to cluster the data. Working through each leaf node in the tree and evaluating the effect of deleting it using a hold-out test set is the quickest and simplest pruning approach.
  • Data preparation for the  CART:  No special data preparation is required for the CART algorithm.

Advantages of CART

  • Results are simplistic.
  • Classification and regression trees are Nonparametric and Nonlinear.
  • Classification and regression trees implicitly perform feature selection.
  • Outliers have no meaningful effect on CART.
  • It requires minimal supervision and produces easy-to-understand models.

Limitations of CART

  • Overfitting.
  • High Variance.
  • low bias.
  • the tree structure may be unstable.

Applications of the CART algorithm

  • For quick Data insights.
  • In Blood Donors Classification.
  • For environmental and ecological data.
  • In the financial sectors.
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