Logistic Regression

Key Concepts

🔹 Step 1: Basic Binary Classification

Predict if an email is spam or not spam

from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
import numpy as np

# Email features: [word_count, exclamation_marks, capital_letters]
X = np.array([
    [50, 0, 5],    # Normal email
    [30, 0, 3],    # Normal email  
    [200, 5, 50],  # Spam email
    [180, 8, 45],  # Spam email
    [40, 1, 8],    # Normal email
    [220, 6, 60]   # Spam email
])

y = [0, 0, 1, 1, 0, 1]  # 0=normal, 1=spam

# Train model
model = LogisticRegression()
model.fit(X, y)

# Test prediction
test_email = [[100, 3, 25]]  # New email features
prediction = model.predict(test_email)[0]
probability = model.predict_proba(test_email)[0][1]

print(f"Prediction: {'Spam' if prediction == 1 else 'Normal'}")
print(f"Spam probability: {probability:.2f}")

🔹 Step 2: Understanding Probabilities

How logistic regression calculates probabilities

# Get probabilities for multiple examples
test_emails = [
    [20, 0, 2],    # Very normal email
    [100, 3, 25],  # Suspicious email
    [300, 10, 80]  # Very spammy email
]

for i, email in enumerate(test_emails):
    probs = model.predict_proba([email])[0]
    normal_prob = probs[0]
    spam_prob = probs[1]
    
    print(f"Email {i+1}:")
    print(f"  Normal probability: {normal_prob:.3f}")
    print(f"  Spam probability: {spam_prob:.3f}")
    print(f"  Prediction: {'Spam' if spam_prob > 0.5 else 'Normal'}")
    print()

# The probabilities always add up to 1.0

🔹 Step 3: Feature Importance

Understanding which features matter most

# Get feature coefficients
coefficients = model.coef_[0]
features = ['word_count', 'exclamation_marks', 'capital_letters']

print("Feature importance (coefficients):")
for feature, coef in zip(features, coefficients):
    print(f"{feature}: {coef:.3f}")

# Positive coefficient = increases spam probability
# Negative coefficient = decreases spam probability
# Larger absolute value = more important feature

# Example interpretation:
# If exclamation_marks has coefficient 0.5:
# Each additional exclamation mark increases spam odds by exp(0.5) ≈ 1.65x

🔹 Step 4: Model Evaluation

Measuring how well the model performs

from sklearn.metrics import accuracy_score, classification_report

# Create larger dataset for proper evaluation
np.random.seed(42)
X_large = np.random.rand(100, 3) * 200  # Random email features
# Create realistic labels based on features
y_large = (X_large[:, 1] > 3) | (X_large[:, 2] > 40)  # Spam if many ! or CAPS

# Split data
X_train, X_test, y_train, y_test = train_test_split(
    X_large, y_large, test_size=0.3, random_state=42
)

# Train and evaluate
model = LogisticRegression()
model.fit(X_train, y_train)
predictions = model.predict(X_test)

# Calculate accuracy
accuracy = accuracy_score(y_test, predictions)
print(f"Accuracy: {accuracy:.2f}")

# Detailed report
print("\nDetailed Report:")
print(classification_report(y_test, predictions, 
                          target_names=['Normal', 'Spam']))

🔹 Step 5: Real-World Example

Medical diagnosis: Predicting disease risk

# Patient data: [age, blood_pressure, cholesterol]
patients = np.array([
    [25, 120, 180],  # Young, healthy
    [45, 140, 220],  # Middle-aged, moderate risk
    [65, 160, 280],  # Older, high risk
    [30, 110, 160],  # Young, very healthy
    [55, 180, 300],  # High risk
    [40, 130, 200]   # Moderate
])

# Disease outcomes (0=healthy, 1=disease)
outcomes = [0, 0, 1, 0, 1, 0]

# Train model
health_model = LogisticRegression()
health_model.fit(patients, outcomes)

# Predict for new patient
new_patient = [[50, 150, 250]]  # 50 years old, BP=150, Chol=250
risk_prob = health_model.predict_proba(new_patient)[0][1]

print(f"Disease risk probability: {risk_prob:.2f}")
if risk_prob > 0.5:
    print("High risk - recommend further testing")
else:
    print("Low risk - routine monitoring")

# This helps doctors make informed decisions