Classification and regression trees (CART) may be a term used to describe decision tree algorithms that are used for classification and regression learning tasks.

CART was introduced in the year 1984 by Leo Breiman, Jerome Friedman, Richard Olshen and Charles Stone for regression task. It is additionally a predictive model which helps to seek out a variable supported other labelled variables. To be more clear the tree models predict the result by asking a group of if-else questions.

Two advantages of using tree model are as follows :

Theyâ€™re ready to capture the non-linearity within the data set.

No need for standardisation of knowledge when using tree models.

Understanding Decision Tree

If you strip it right down to the fundamentals, decision tree algorithms are nothing but if-else statements which will be wont to predict a result supported data.

Machine learning algorithms are often classified into two types- supervised and unsupervised. a choice tree may be a supervised machine learning algorithm. itâ€™s a tree-like structure with its root node at the highest.

The many names wont to describe the CART algorithm for machine learning.

The representation employed by learned CART models that are stored on disk.

How a CART model is often learned from training data.

How a learned CART model is often wont to make predictions on unseen data.

Additional resources that you simply can use to find out more about CART and related algorithms.

Decision Trees are commonly utilised in data processing with the target of making a model that predicts the worth of a target (or dependent variable) supported the values of several inputs (or independent variables).

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CART(Classification And Regression Tree) for Decision Tree

The CART or Classification & Regression Trees methodology refers to those two sorts of decision trees. While there are many classification and regression trees tutorials, videos and classification and regression trees there may be a simple definition of the two sorts of decisions trees. It also includes classification and regression trees examples.

Decision trees in the following categories are together referred to as CART:

Classification trees: When the required value is continuous, this tree is used to find the "class" into which it is most likely to fall.

Regression trees: To forecast a continuous variable's value, regression trees are used.

Classification Trees

It is an algorithm where the target variable is always fixed or categorical. The algorithm is then used to identify the â€śclassâ€ť within which a target variable would presumably fall into. An example of a classification-type problem would be determining who will or wonâ€™t subscribe to a digital platform; or who will or wonâ€™t graduate from high school.

These are samples of simple binary classifications where the specific variable can assume just one of two, mutually exclusive values. In other cases, you would possibly need to predict among a variety of various variables. as an example, youâ€™ll need to predict which sort of smartphone a consumer may plan to purchase. In such cases, there are multiple values for the specific variable. Hereâ€™s what a classic classification tree seems like.

Regression Trees

A regression tree refers to an algorithm where the target variable is and therefore the algorithm is employed to predict itâ€™s value. As an example of a regression type problem, youâ€™ll want to predict the selling prices of a residential house, which may be a continuous variable.

This will depend upon both continuous factors like square footage also as categorical factors just like the sort of home, area during which the property is found then on.

CART Algorithm

The CART (Classification and Regression Trees) algorithm is a decision tree-based machine learning technique used for both classification and regression tasks.

Tree Structure: CART constructs a binary tree structure where each internal node represents a decision based on a feature's value, and each leaf node corresponds to a class label (for classification) or a predicted value (for regression).

Splitting Criteria: At each node, CART selects the feature and the value to split the dataset into two subsets. It chooses the split that maximizes the homogeneity or purity of the resulting subsets, typically measured by metrics like Gini impurity for classification or mean squared error for regression.

Pruning: After constructing the tree, pruning is performed to avoid overfitting. Pruning involves removing branches (subtrees) that provide little predictive power on unseen data. It helps simplify the tree while retaining its predictive accuracy, usually by using techniques like cost-complexity pruning.

How does CART algorithm works?

The CART (Classification and Regression Trees) algorithm works by recursively partitioning the input data into subsets based on the values of features, ultimately creating a decision tree that can be used for classification or regression tasks.

Initial Split: CART starts by selecting the feature and the value that best splits the dataset into two subsets, maximizing the homogeneity of the resulting subsets.

Recursive Partitioning: It continues this process recursively for each subset, creating binary splits at each node until a stopping criterion is met. The stopping criterion could be reaching a maximum tree depth, having minimum instances in a node, or other conditions to prevent overfitting.

Splitting Criteria: CART uses splitting criteria such as Gini impurity for classification tasks and mean squared error for regression tasks to determine the optimal feature and value for partitioning the data.

Tree Pruning: After constructing the full tree, CART may prune it to prevent overfitting. Pruning involves removing branches or nodes that contribute little to the predictive accuracy of the tree on unseen data.

Prediction: Once the tree is constructed, it can be used for prediction. For classification, the input data traverses the tree from the root to a leaf node, where the majority class in that node determines the predicted class. For regression, the predicted value is typically the average of the target values in the leaf node.

Calculating Gini Index

For classification and regression problems, decision tree-supervised Machine Learning algorithms perform well. The probability that a particular variable would be misclassified when chosen at random is determined by the Gini index, also referred to as the Gini coefficient or Gini impurity. The Gini index has a degree range of 0 to 1.

Where 0 denotes the presence of a single class or the fact that all objects fall under that class.

When the Gini index is 1, all the items are dispersed randomly among the classes.

When the Gini index is 0.5, the elements are distributed evenly among many classes.

CART models from Data

A binary tree serves as the CART model's representation. A single input variable (x) and a split point on that variable are represented by each root node (assuming the variable is numeric). A prediction is made using the output variable (y) in the tree's leaf nodes. Selecting input variables and split points on those variables is necessary to build an appropriate tree when building a CART model. A greedy algorithm is used to optimize a cost function, choosing the input variable to utilize and the precise split or cut-point. A predetermined ending criterion, such as the minimum number of training instances allotted to each tree leaf node, determines when a tree is complete.

Greedy Algorithm

In reality, the process of splitting up the input space is what goes into creating a binary decision tree. The space is split using a method known as recursive binary splitting, which is greedy. In this numerical process, various split points are explored and tested using a cost function as all the numbers are lined up. We choose the split with the bestâ€”the lowest cost since we reduce costs. A greedy evaluation and selection process considers all input variables and all potential split points (e.g., the very best split point is chosen each time).

The sum squared error across all training samples that fall within the rectangle is the cost function that is minimized to identify split points for regression predictive modeling problems: sum(y â€“ prediction)^2 where y represents the result for the training sample and prediction represents the expected result for the rectangle.

Stopping Criterion

When it descends the tree with the training data, the recursive binary splitting algorithm mentioned above must know when to stop splitting.

Using a minimal count on the number of training instances provided to each leaf node is the most popular halting strategy. The split is rejected and the node is treated as a final leaf node if the count is less than a certain minimum. The number of training participants is adjusted to the dataset, for example, 10 or 20. It specifies how specialized the tree will be to the training set of data.

Tree pruning

The stopping criterion is crucial because it significantly affects how well your tree performs. After becoming familiar with your tree, pruning can help you perform even better. The number of splits in a decision tree is used to describe the complexity of the tree. We want trees that are simpler. There are more advanced pruning techniques that can be utilised, such as weakest link pruning or cost complexity pruning, where the size of the sub-tree is used to determine if nodes can be deleted.

Data preparation for CART algorithm

Apart from a strong problem representation, CART requires no specific data preparation. If the problem is represented with a better model and in a clear way, then special representation is not needed.

Difference Between Classification and Regression Trees

Basis

Classification Trees

Regression Trees

When to use

Classification trees are mostly used when the dataset must be split into classes, part of the response variable.

Regression trees are used when the response variable is continuous. as an example, if the response variable is some things just like the price of a property or the temperature of the day, a regression tree is employed.

Working

A classification tree splits the dataset to support the homogeneity of knowledge. If the training data shows that 95% of individuals older than 30 bought the phone, the info gets split there, and age becomes a top node within the tree. This split makes the info â€ś95% pureâ€ť

In a regression tree, a regression model fits the target variable using each independent variable. After this, the info is split at several points for every experimental variable. At each such point, the error between the anticipated, and actual values is squared to urge â€śA Sum of Squared Errorsâ€ť(SSE).

The representation for the CART model may be a binary tree. This is a binary tree which is formed from the algorithms and data structures which is nothing too fancy. Each root node represents one input variable (x) and a split point thereon variable (assuming the variable is numeric).

The leaf nodes of the tree contain an output variable (y) which is employed to form a prediction. Given a dataset with two inputs (x) of height in centimetres and weight in kilograms the output of sex as male or female, below may be an example of a binary decision tree which is completely fictitious for demonstration purposes only and is very important.

Decision Tree CART Implementations

Implementations of the CART (Classification and Regression Trees) algorithm involve translating the theoretical concepts into practical code for building decision trees. Several programming languages and libraries offer implementations of CART for both classification and regression tasks.

Programming Languages

Python: Python is a popular choice for implementing CART due to its extensive libraries for machine learning and data manipulation. Libraries such as scikit-learn provide efficient implementations of CART algorithms for both classification (e.g., DecisionTreeClassifier) and regression (e.g., DecisionTreeRegressor) tasks.

R: R is another widely used language for statistical computing and machine learning. The "rpart" package in R offers an implementation of the CART algorithm for creating decision trees.

Libraries and Packages

scikit-learn: scikit-learn is a machine learning library in Python that provides a comprehensive set of tools for various tasks, including CART. Its DecisionTreeClassifier and DecisionTreeRegressor classes enable users to create decision trees using the CART algorithm.

Rpart: The "rpart" package in R provides functions for building decision trees using the CART algorithm. Users can specify parameters such as splitting criteria, pruning methods, and tree complexity to customize the tree-building process.

Features

Flexibility: CART implementations typically offer flexibility in terms of customizing the tree-building process. Users can specify parameters such as the maximum tree depth, minimum samples per leaf, and splitting criteria to tailor the decision tree to their specific needs.

Efficiency: Implementations of CART algorithms are designed to be efficient and scalable, allowing them to handle large datasets with millions of samples and thousands of features.

Visualization: Many CART implementations include functionality for visualizing the resulting decision tree, which helps users interpret the model and understand how input features contribute to predictions.

Advantages of CART

Classification and regression trees work to supply accurate predictions or predicted classifications, supported the set of if-else conditions. They typically have several advantages over regular decision trees.

The Results are Simplistic: The interpretation of results summarised in classification or regression trees is typically fairly simple. It allows for the rapid classification of the latest observations. Thatâ€™s because itâ€™s much simpler to gauge only one or two logical conditions than to compute scores using complex nonlinear equations for every group. It can often end in an easier model which explains why the observations are either classified or predicted in a certain way. as an example, business problems are much easier to elucidate with if-then statements than with complex nonlinear equations.

Classification and Regression Trees are one of Nonparametric or distribution-free & Nonlinear: The results from classification and regression trees are often summarized in simplistic if-then conditions. This negates the necessity for the subsequent implicit assumptions.

Classification and regression tree methods are compatible with data processing. This is often because thereâ€™s little or no knowledge or assumptions which will be made beforehand about how the various variables are related.

Limitations of CART Algorithm

Classification and regression tree tutorials, also as classification and regression tree ppts, exist in abundance. this is often a testament to the recognition of those decision trees and the way frequently theyâ€™re used. However, these decision trees arenâ€™t without their disadvantages.

The applications of the CART algorithm are following:

Classification and regression Decision Trees are frequently created using CART.

To discover correlations between attributes, the CART model is utilized.

In data mining, decision trees are frequently used to build models that forecast the value of a goal based on the values of numerous input variables (or independent variables).

The enlarged definition for identifying regular voluntary donors and the CART-derived model gave rise to a solid classification accuracy-based model.

Psychiatric outpatients with low income who would be high-service consumers were found using CART.

Frequently Asked Questions

What is classification tree also known as?

Classification tree is also known as a decision tree, used for partitioning data into classes based on feature values.

What are the benefits of classification and regression trees?

Benefits of classification and regression trees include interpretability, handling non-linear relationships, and handling mixed data types effectively.

What is a classification tree in statistics?

In statistics, a classification tree is a predictive modeling tool that partitions data into subsets based on predictor variables to predict categorical outcomes.

Which trees can be used for both regression and classification?

Decision trees, particularly those using algorithms like CART (Classification and Regression Trees), can be used for both regression and classification tasks.

What is cart classification method?

A predictive model called a Classification And Regression Tree (CART) describes how the values of an outcome variable can be predicted based on the values of other variables. It illustrates how the values of the target variable can be predicted using information from other variables.

What is the measure for cart algorithm?

Gini Index is used by CART (Classification algorithm and Regression Trees) as a tool for attribute selection. The Gini index, also known as the Gini coefficient or Gini impurity, calculates the likelihood that a given variable will be incorrectly classified when selected randomly.

What does cart stand for in decision tree?

Classification And Regression Trees, often known as CART. Decision tree algorithms used for classification and regression learning tasks are sometimes referred to as classification and regression trees (CART). The representation for the CART model may be a binary tree.

Conclusion

In this blog, we discussed Classification and Regression Trees(CART). Then we saw each of the topics in detail. We also saw CART Algorithm, Gini Index, CART models from Data, Difference Between Classification and Regression Trees. Ultimately, we discussed the CART Model Representation, Advantages, Limitations, and applications of CART.