# Decision Tree

## Understanding Decision Trees in Machine Learning

Decision Trees are a non-parametric supervised learning method used for both classification and regression tasks. The goal is to create a model that predicts the value of a target variable by learning simple decision rules inferred from the data features.

### How Decision Trees Work

A decision tree is constructed by recursively partitioning the input data into subsets based on the value of a single attribute. This process is akin to asking a series of questions, each of which splits the data into two or more groups based on the answers. These questions are formed by selecting attributes and threshold values that effectively segregate the data.

The tree itself is a binary tree structure, where each node represents a "question" or "test" of an attribute, each branch represents the outcome of the test, and each leaf node represents a class label or a regression value. The topmost node in a tree is known as the root node. It learns to partition on the basis of the attribute that provides the maximum information gain. Information gain is often measured by the decrease in entropy or Gini impurity.

### Entropy and Information Gain

Entropy is a measure of disorder or uncertainty and the goal of machine learning models and, in the context of decision trees, it is to reduce this uncertainty. A tree that is well constructed will have an entropy of zero, meaning that the samples within each leaf node are completely homogeneous.

Information gain is a measure of the difference in entropy from before to after the set is split on an attribute. It is used to decide which attribute to split on at each step in building the tree.

### Gini Impurity

Gini impurity is another measure used in decision trees, particularly the CART (Classification and Regression Trees) algorithm. It represents the probability of a random sample being incorrectly labeled if it was randomly labeled according to the distribution of labels in the subset. The best attribute chosen to split the data is the one that decreases the Gini impurity the most.

### Pruning

Pruning is a technique in machine learning that reduces the size of decision trees by removing sections of the tree that provide little power in predicting target variables. This is done to simplify the model and avoid overfitting. Overfitting occurs when the tree is designed so as to perfectly fit all samples in the training data set, which may negatively impact the model's ability to generalize from the training data to unseen data.

• Simple to understand and interpret: Trees can be visualised, which makes them easy to interpret even for people without expertise in machine learning.
• Requires little data preparation:

Other techniques often require data normalization, dummy variables need to be created and blank values to be removed. None of these steps are required for decision trees.

• The cost of using the tree for prediction is logarithmic: In the number of data points used to train the tree.
• Able to handle multi-output problems: Decision trees can predict several variables of the data that are not necessarily correlated.

Despite their advantages, decision trees also have some limitations:

• Overfitting: Without proper pruning, they can create overly complex trees that do not generalize well from the training data.
• Instability: Small variations in the data can result in a completely different tree being generated.
• Biased Trees: If some classes dominate, decision trees learners can create biased trees. It is therefore recommended to balance the dataset prior to fitting with the decision tree.

### Applications of Decision Trees

Decision trees are versatile algorithms that can be used in a variety of contexts. They are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal. In machine learning, they serve as a predictive model to go from observations about an item to conclusions about the item's target value.

In the realm of business and management, decision trees are used for strategic planning and operational decision-making. In finance, they can be used to assess the risk of lending to a borrower or in investment strategies. In healthcare, decision trees can help in diagnosing diseases based on symptoms and patient history.

### Conclusion

Decision Trees are a powerful tool in the machine learning toolkit. They are easy to interpret, can handle a variety of data types, and are computationally efficient. However, care must be taken to avoid overfitting and to ensure that the trees are robust to changes in the data. With the right precautions, decision trees can provide valuable insights and predictions across a wide range of disciplines.