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MachineLearning/decisionTree.md

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+id: decision-tree  
+title: Decision Tree Algorithm  
+sidebar_label: Decision Tree  
+description: "In this post, we'll explore the Decision Tree Algorithm, a popular machine learning model used for classification and regression tasks."  
+tags: [machine learning, algorithms, decision tree, classification, regression]
+
+---
+
+### Definition:
+The **Decision Tree Algorithm** is a supervised machine learning algorithm used for both **classification** and **regression** tasks. It splits data into subsets based on feature values, creating a tree-like structure where each internal node represents a decision based on a feature, and each leaf node represents an outcome (class label or continuous value).
+
+### Characteristics:
+- **Recursive Partitioning**:  
+  A decision tree recursively splits the dataset based on specific conditions (features) to form a tree structure that leads to a prediction at each leaf node.
+
+- **Interpretability**:  
+  Decision trees are highly interpretable because the decision-making process is clear and transparent. You can easily follow the path of decisions from root to leaf to understand how a prediction is made.
+
+- **Non-parametric**:  
+  This algorithm doesn’t make any assumptions about the underlying data distribution, making it suitable for a variety of datasets.
+
+### Types of Decision Trees:
+1. **Classification Tree**:  
+   Used when the target variable is categorical (e.g., yes/no, spam/ham). It predicts the class label based on the features.
+
+2. **Regression Tree**:  
+   Used when the target variable is continuous (e.g., predicting a price). It predicts a real number based on the features.
+
+### Steps Involved:
+1. **Choose the Best Split**:  
+   The dataset is split based on the feature that maximizes some criteria. For classification, **Gini Index** or **Entropy** (used in information gain) is commonly used. For regression, **mean squared error** is often the criterion.
+
+2. **Recursively Split**:  
+   The process is repeated recursively for each subset, creating branches until no further meaningful splits can be made (e.g., when the data is perfectly classified or a stopping criterion like maximum depth is reached).
+
+3. **Assign Leaf Nodes**:  
+   Once the splitting stops, the leaf nodes are assigned a class label (for classification) or a value (for regression).
+
+### Problem Statement:
+Given a dataset with features and target values, the goal is to build a decision tree that can **classify** data points into categories or **predict** continuous values based on the features. 
+
+### Key Concepts:
+- **Root Node**:  
+  The top-most node in the tree, where the first feature split occurs.
+
+- **Internal Nodes**:  
+  Nodes where further feature splits occur based on the conditions.
+
+- **Leaf Nodes**:  
+  Terminal nodes that hold the final prediction (class or value).
+
+### Split Criteria:
+- **Gini Impurity** (for classification):  
+  Measures the probability of a randomly chosen element being misclassified.
+
+![image](https://github.com/user-attachments/assets/505d8d21-3f41-4bba-9120-4ad98beec8c1)
+
+
+  Where \( p_i \) is the probability of the class label at node \( i \).
+
+- **Entropy** (for classification):  
+  Measures the disorder or impurity in the dataset.
+
+![image](https://github.com/user-attachments/assets/954fa9ab-f3d6-4055-8c12-7630dd8e6a50)
+
+
+  Where \( p_i \) is the proportion of data points in class \( i \).
+
+- **Information Gain**:  
+  Measures the reduction in entropy after a dataset is split on a feature.
+
+![image](https://github.com/user-attachments/assets/e0eecef3-6e4d-414c-a963-19708922ed91)
+
+
+- **Mean Squared Error (MSE)** (for regression):  
+  Measures the variance between the predicted and actual values at each node.
+
+### Time Complexity:
+- **Best, Average, and Worst Case: $O(n \log n)$**  
+  The time complexity depends on sorting the dataset at each node. For `n` data points, the overall complexity is logarithmic in depth with respect to the size of the dataset.
+
+### Space Complexity:
+- **Space Complexity: $O(n)$**  
+  The space complexity arises from storing the tree structure and the data used for training.
+
+### Example:
+Consider a dataset for predicting whether someone buys a product based on their **age** and **income**:
+
+- Dataset:
+  ```  
+  | Age   | Income  | Buys Product |  
+  |-------|---------|--------------|  
+  | 25    | High    | Yes          |  
+  | 45    | Medium  | No           |  
+  | 35    | Low     | Yes          |  
+  | 22    | Low     | Yes          |  
+  ```
+
+Step-by-Step Execution:
+
+1. **Choose the best split**:  
+   Using a criterion like Gini Impurity or Information Gain, the algorithm will decide which feature (Age or Income) provides the best split.
+
+2. **Recursively split**:  
+   It splits the data and continues until leaf nodes are formed, which represent the final decision (Yes/No for classification).
+
+### Python Implementation:
+Here is a basic implementation of a Decision Tree in Python using **scikit-learn**:
+
+```python
+from sklearn.datasets import load_iris
+from sklearn.tree import DecisionTreeClassifier
+from sklearn import tree
+import matplotlib.pyplot as plt
+
+# Load dataset
+iris = load_iris()
+X, y = iris.data, iris.target
+
+# Create Decision Tree classifier
+clf = DecisionTreeClassifier()
+
+# Train model
+clf = clf.fit(X, y)
+
+# Plot the tree
+plt.figure(figsize=(12,8))
+tree.plot_tree(clf, filled=True, feature_names=iris.feature_names, class_names=iris.target_names)
+plt.show()
+```
+
+### Summary:
+The **Decision Tree Algorithm** is a simple yet powerful model that can be used for both classification and regression tasks. Its ease of interpretation, ability to handle both categorical and numerical data, and non-parametric nature make it a versatile choice for many machine learning problems. However, decision trees are prone to **overfitting**, which can be mitigated by techniques like **pruning**, **random forests**, or **ensemble methods**.
+