OLS的目标函数: J ( w ) = ∑ j = 1 N ( y i − f ( x i ) ) 2 J(w) = \sum_{j=1}^N(y_i - f(x_i))^2 J(w)=∑j=1N(yi−f(xi))2
岭回归的目标函数: J ( w ; λ ) = ∑ i = 1 N ( y i − f ( x i ) ) 2 + λ ∑ j = 1 D w j 2 ) J(w; \lambda) = \sum_{i=1}^N(y_i - f(x_i))^2 + \lambda \sum_{j=1}^D w_j^2) J(w;λ)=∑i=1N(yi−f(xi))2+λ∑j=1Dwj2)
Lasso回归的目标函数: J ( w ; λ ) = ∑ i = 1 N ( y i − f ( x i ) ) 2 + λ ∑ j = 1 D ∣ w j ∣ J(w;\lambda) = \sum_{i=1}^N (y_i - f(x_i))^2 + \lambda \sum_{j=1}^D |w_j| J(w;λ)=∑i=1N(yi−f(xi))2+λ∑j=1D∣wj∣