Ridge regression prevents overfitting through the use of a regularization term in its loss function. Here's how it works:
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Regularization Term: Ridge regression adds a penalty term to the ordinary least squares loss function, which is proportional to the square of the coefficients (L2 norm). The modified loss function is:
[
\text{Loss} = \text{Sum of Squared Errors} + \alpha \sum_{j=1}^{p} \beta_j^2
]
where (\alpha) is the regularization parameter, and (\beta_j) are the coefficients. -
Coefficient Shrinkage: The penalty term discourages large coefficients by penalizing their size. This shrinkage helps to simplify the model, making it less sensitive to fluctuations in the training data.
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Bias-Variance Tradeoff: By introducing bias through regularization, ridge regression reduces variance, which is often a major contributor to overfitting. A simpler model is less likely to capture noise in the training data.
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Stability: Ridge regression is particularly effective in situations where features are highly correlated (multicollinearity). The regularization helps stabilize the estimates of the coefficients, leading to more reliable predictions.
Overall, by controlling the complexity of the model, ridge regression enhances its ability to generalize to new, unseen data, thereby reducing the risk of overfitting.
