Supervised Learning — Classification

Contents

1. Logistic Regression
2. Naive Bayes Classifier
3. Decision Tree Classifier

Logistic Regression

Though the name has regression in it , Logistic regression is a classification algorithm that is used to perform binary classification tasks . (0 or 1) , (Yes or No ) , (True or False).

e.g. Predicting whether a customer will buy a product (Yes/No) based on their profile is an example of Binomial Logistic Regression.

Why Use Logistic Regression:

Bounded output (0 to 1)

• Uses the sigmoid (logistic) function to ensure outputs are between 0 and 1.
• Output can be interpreted as a probability of the positive class.

Natural thresholding

• We can set a threshold (e.g., 0.5) to decide the class:
  If above 0.5 → positive class , else → negative class

Better loss function

• Logistic regression uses log loss (cross-entropy), which is ideal for classification tasks, unlike the squared error in linear regression.

Naive Bayes Classifier

Uses Bayes algorithm to classify data based on probabilities.
‘Naive’ → the presence of one feature does not affect the others.

Assumptions

1. Feature independence
2. All features are equally important
3. No missing data

Bayes Theorem

e.g. Golf Playing prediction

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Data to be classified: X = (outlook =Sunny, Temperature = Mild, Humidity = Windy = False)

Naive Bayes

Since P(C1|X) > P(C2|X ) , play_golf = Yes

Decision Tree

A Decision Tree Classifier is a supervised learning algorithm used for both classification (categorical targets) and regression (continuous targets) tasks. It builds a model in the shape of a tree structure, where data is split into branches based on feature values, leading to a series of decisions that ultimately assign a class label or value to each data point.

CART: Classification and Regression Trees

CART (Classification and Regression Trees) is a popular framework for constructing decision trees:

• Classification Trees: Used when the target variable is categorical (e.g., classifying emails as spam or not spam).
• Regression Trees: Used when the target variable is continuous (e.g., predicting house prices).

Decision Tree Structure

A decision tree consists of:

• Root Node: The initial node representing the entire dataset.
• Internal Nodes: Nodes where decisions are made based on feature values.
• Branches: Outcomes of decisions, leading to further nodes.
• Leaf Nodes: Terminal nodes that assign a class label (for classification) or a value (for regression).

Steps to Build a Decision Tree

1. Select the Best Feature to Split

• For classification, use impurity measures such as Gini Impurity or Entropy to evaluate how well a feature separates the classes.
• For regression, use metrics like Mean Squared Error (MSE) to assess splits.

2. Split the Data

• Partition the data into subsets based on the chosen feature and its value(s).

3. Repeat the Process Recursively

• For each subset, repeat the process: select the next best feature and split again, forming a recursive, top-down tree structure.

4. Assign Labels to Leaf Nodes

• Once further splitting no longer improves homogeneity (purity) or a stopping criterion is met, assign the majority class (classification) or average value (regression) to the leaf node.

Impurity Measures for Splitting

• Gini Impurity: Measures the probability of misclassifying a randomly chosen element.
• Entropy: Measures the amount of information disorder or unpredictability.