Answer-first summary for fast verification
Answer: The ridge is known as the L2 regularization because of the second-order natures of the shrinkage term, and it helps avoid situations where the parameter estimates are offsetting, with one having a large positive value and another a large negative value.
## Explanation Let's analyze each option: **Option A**: Incorrect. LASSO is indeed L1 regularization (uses L1 norm), but it can set coefficients exactly to zero, not just make them closer to zero. This feature selection property is a key advantage of LASSO. **Option B**: Incorrect. Ridge regression is L2 regularization (uses L2 norm), not L1. Also, ridge regression shrinks coefficients toward zero but doesn't set them exactly to zero. **Option C**: Incorrect. LASSO is L1 regularization, not L2. While it does remove less important features by setting their coefficients to zero, the regularization type is misidentified. **Option D**: **Correct**. Ridge regression is L2 regularization (uses L2 norm penalty), and it helps prevent multicollinearity issues where correlated variables have offsetting large positive and negative coefficients. The L2 penalty discourages extreme coefficient values. ### Key Differences: - **LASSO (L1)**: Uses absolute value penalty, can perform feature selection by setting coefficients to exactly zero - **Ridge (L2)**: Uses squared penalty, shrinks coefficients but doesn't set them to zero, helps with multicollinearity Option D accurately describes ridge regression as L2 regularization and its benefit in handling correlated features.
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Regularization is an approach for ensuring that models do not become too large or complex, and it is particularly useful when there is a large number of highly correlated features. Two widely-used regularization methods are known as the ridge and the LASSO (the least absolute shrinkage and selection operator). Which of the following statements correctly describe these two methods and their applications?
A
The LASSO is known as the L1 regularization because of the first-order natures of the shrinkage term, and it is used to reduce the magnitude of the parameters, making them closer to, but not equal to, zero.
B
The ridge is known as the L1 regularization because of the first-order natures of the shrinkage term, and it is used to set some of the less-important parameter estimates to zero.
C
The LASSO is known as the L2 regularization because of the second-order natures of the shrinkage term, and it is used to remove less important features.
D
The ridge is known as the L2 regularization because of the second-order natures of the shrinkage term, and it helps avoid situations where the parameter estimates are offsetting, with one having a large positive value and another a large negative value.
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