3 B] What is regularization? How does regularization help in reducing overfitting?
What is Regularization?
Regularization is a technique in machine learning used to prevent overfitting by introducing additional constraints or penalties into the training process. Overfitting occurs when a model learns the noise or irrelevant patterns in the training data, leading to poor performance on unseen data. Regularization helps the model generalize better by discouraging overly complex solutions.
How Regularization Helps Reduce Overfitting
- Penalizing Large Weights:
- Regularization methods add a penalty to the model’s loss function, discouraging the optimization process from assigning large values to weights.
- Models with smaller weights tend to be simpler and less prone to overfitting.
- Encouraging Simplicity:
- Regularization encourages simpler models that are less sensitive to minor fluctuations in the training data.
- This helps the model focus on capturing the general structure of the data rather than memorizing it.
- Stabilizing Training:
- Regularization can make underdetermined problems well-posed by ensuring the optimization problem has a unique solution.
- This prevents issues like numerical instability or infinite weight growth during training.
Types of Regularization
- L1 Regularization (Lasso):
- Adds the sum of the absolute values of the weights as a penalty.
- Encourages sparsity in the model (many weights become exactly zero), which can aid in feature selection.
- L2 Regularization (Ridge):
- Adds the sum of the squared values of the weights as a penalty.
- Encourages small but nonzero weights, leading to smoother models.
- Elastic Net:
- Combines L1 and L2 regularization, balancing sparsity and smoothness.
- Dropout:
- Randomly “drops” a fraction of neurons during training, forcing the model to rely on multiple pathways for making predictions and reducing overfitting.
- Weight Decay:
- Similar to L2 regularization, directly penalizes large weights during gradient updates.
Why Regularization is Necessary in Some Cases
- Underdetermined Problems:
- In linear models like linear regression or PCA, regularization ensures the matrix XTX is invertible. Without regularization, this matrix may become singular, making it impossible to compute solutions directly.
- Infinite Solutions:
- In problems like logistic regression with linearly separable data, the model may find multiple weight vectors that achieve perfect classification. Regularization prevents weights from growing indefinitely by introducing constraints.
- Numerical Stability:
- Regularization ensures convergence during optimization by stabilizing the iterative process, especially for underdetermined or high-dimensional problems.