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Absolutely! Logistic Regression is a popular algorithm used for classification, not regression—despite its name!
🔐 What is Logistic Regression?
Logistic regression models the probability that a given input belongs to a particular class (typically binary: 0 or 1) by using a sigmoid function to output values between 0 and 1.
📊 Use Case Example:
- Email classification: Spam (1) or Not Spam (0)
- Disease prediction: Sick (1) or Healthy (0)
🔹 Model Formula:
It starts like linear regression:
z=w1x1+w2x2+⋯+wnxn+bz = w_1x_1 + w_2x_2 + \dots + w_nx_n + b
Then applies the sigmoid function:
y^=σ(z)=11+e−z\hat{y} = \sigma(z) = \frac{1}{1 + e^{-z}}
Where:
- y^\hat{y} is the predicted probability (between 0 and 1)
- If y^>0.5\hat{y} > 0.5, classify as 1; otherwise, 0
🔸 Loss Function:
- Uses Binary Cross-Entropy (Log Loss):
Loss=−[ylog(y^)+(1−y)log(1−y^)]\text{Loss} = -\left[y \log(\hat{y}) + (1 - y) \log(1 - \hat{y})\right]
✅ Pros:
- Simple and fast
- Outputs probabilities
- Interpretable coefficients
- Works well with linearly separable data
❌ Cons:
- Assumes linear decision boundary
- Doesn’t perform well on complex or non-linear problems without feature engineering or transformation
📦 Extensions:
- Multinomial Logistic Regression: For multi-class problems
- Regularized Logistic Regression: Adds L1 (Lasso) or L2 (Ridge) to prevent overfitting
Would you like a visual of the sigmoid function or a 2D decision boundary example?