Casualty Actuarial Society MAS-1 Practice Exam

In lasso regression, the penalty term uses the L1 norm, which is the sum of the absolute values of the coefficients. This choice is key because the L1 penalty tends to produce sparse solutions, pushing some coefficients to exactly zero, effectively selecting a subset of features. The geometry of the L1 ball has corners aligned with the axes, making it more likely for the optimization to hit a point where some coefficients are zero when combined with the least-squares objective. By contrast, an L2 penalty (ridge) shrinks coefficients but rarely makes them exactly zero, since it uses the sum of squares. L0 focuses on the count of nonzero coefficients and is non-convex and hard to optimize, while L∞ would constrain the largest coefficient in absolute value, not create sparsity in the same way. Hence, the penalty term in lasso is the L1 norm.