What penalty term does lasso regression use?

What penalty term does lasso regression use?

• A. L2 norm penalty (sum of squares)
• B. No penalty
• C. L∞ norm penalty
• D. L1 norm penalty (sum of absolute values)

Answer: (D)

Lasso regression uses an L1 penalty on the coefficients. In the objective, you minimize the usual least squares error plus a penalty term that is lambda times the sum of the absolute values of the coefficients. This L1 penalty tends to shrink some coefficients all the way to zero, which effectively performs feature selection. That sparsity behavior is what sets lasso apart from ridge regression, which uses the L2 penalty (sum of squares) and typically reduces coefficients but rarely makes them exactly zero. An L∞ penalty would focus on the maximum absolute coefficient, which is not how lasso is formulated, and having no penalty corresponds to ordinary least squares with no regularization. So the penalty term is the L1 norm, the sum of absolute values.

Lasso regression uses an L1 penalty on the coefficients. In the objective, you minimize the usual least squares error plus a penalty term that is lambda times the sum of the absolute values of the coefficients. This L1 penalty tends to shrink some coefficients all the way to zero, which effectively performs feature selection. That sparsity behavior is what sets lasso apart from ridge regression, which uses the L2 penalty (sum of squares) and typically reduces coefficients but rarely makes them exactly zero. An L∞ penalty would focus on the maximum absolute coefficient, which is not how lasso is formulated, and having no penalty corresponds to ordinary least squares with no regularization. So the penalty term is the L1 norm, the sum of absolute values.