Regularization

Control overfitting by penalizing large weights. Compare L1 and L2 intuitively.

Interactive simulation

Bias-variance tradeoff controls

Regularization strength λ0.20

Current weight w1.40

Data noise0.30

Current loss

0.542

Penalty term

0.392

Bias effect

Low

Variance effect

Higher variance

Chart

Mathematical intuition

\mathcal{L}=\mathcal{L}_{data}+\lambda\|w\|_1

\mathcal{L}=\mathcal{L}_{data}+\lambda\|w\|_2^2

L1 encourages sparsity (some weights exactly zero). L2 shrinks all weights smoothly.

Step-by-step workflow

Input → Processing → Learning → Prediction → Output

Input

Features + labels

Processing

Compute data loss

Learning

Add penalty and optimize

Prediction

Use shrunk parameters

Output

More stable generalization

Code implementation

python

# L2 ridge objective
loss = mse(y_true, y_pred) + lam * (w**2).sum()

# L1 lasso objective
loss = mse(y_true, y_pred) + lam * abs(w).sum()

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