When and why not to us regularisation

While regularization is tool to combat overfitting, it is not a always useful. It is crucial to consider the model’s

• complexity,
• the quality and
• quantity of data,
• and the appropriateness of the regularization parameters

to ensure effective performance on validation data. If your model is performing well on training data but poorly on validation data, regularization might not always solve this issue for several reasons:

1. Underfitting: While regularization aims to reduce overfitting, it can also lead to underfitting if the penalty is too strong. This occurs when the model becomes too simplistic and fails to capture the underlying patterns in the data, resulting in poor performance on both training and validation datasets.

2. Model Complexity: Regularization primarily addresses the complexity of the model. If the model architecture itself is not suitable for the task (e.g., too simple or inappropriate for the data distribution), regularization won’t help improve performance. The model may still struggle to learn the necessary features, leading to poor validation performance.

3. Insufficient Data: If the training dataset is small or not representative of the validation dataset, regularization may not compensate for the lack of data. The model might learn noise or irrelevant patterns from the training data, which regularization cannot correct.

4. Improper Regularization Parameter ($\lambda$): The effectiveness of regularization depends on the choice of the regularization parameter $\lambda$. If $\lambda$ is set too high, it can overly penalize the model’s parameters, leading to underfitting. Conversely, if it’s too low, it may not sufficiently reduce overfitting.

5. Feature Interaction: Regularization techniques like $L_1$ and $L_2$ may not effectively capture complex interactions between features. If the relationships in the data are intricate, regularization alone may not improve the model’s ability to generalize.

6. Validation Set Issues: The validation set itself may not be representative of the problem space, or it may contain noise or outliers that affect the model’s performance. Regularization won’t address these issues if the validation data is flawed.