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Logistic Discrimination and Its Application in Binary Classification

Logistic Discrimination, also known as Logistic Regression, is a statistical method used for binary classification tasks. Unlike linear regression, which predicts continuous values, logistic regression predicts probabilities of class membership using the sigmoid function.

Concept of Logistic Discrimination

• The model estimates the probability that a given input $X$ belongs to class 1 (positive class) or 0 (negative class).

• The prediction is based on a linear combination of features, passed through a sigmoid function:

  $$P(Y = 1 | X) = \frac{1}{1 + e^{-(w^T X + b)}}$$

  where:

  • $X$ is the feature vector,

  • $w$ is the weight vector,

  • $b$ is the bias,

  • The sigmoid function maps values to a probability range (0,1).

• The decision rule is:

  • If $P(Y = 1 | X) > 0.5$, classify as 1 (positive).

  • Else, classify as 0 (negative).

Application in Binary Classification

1. Spam Detection: Classifies emails as spam or not spam.

2. Medical Diagnosis: Predicts if a patient has a disease (1) or not (0).

3. Credit Scoring: Determines if a loan applicant is high-risk or low-risk.

4. Fraud Detection: Identifies fraudulent transactions.

Advantages

• Interpretable: Easy to understand and implement.

• Probabilistic Output: Useful for threshold-based decision-making.

• Less Prone to Overfitting: Especially with regularization techniques.

Logistic discrimination is a foundational method in machine learning and statistics, widely used in real-world classification problems.