structural:scholar_edition
Making λ easier to interpret with an accuracy-simplicity tradeoff

For p = 1 {\displaystyle p=1}, the moment of activation is again given by λ ~ lasso, i = R 2 {\displaystyle {\tilde {\lambda }}_{{\text{lasso}},i}=R^{2}}. If β 0 {\displaystyle \beta _{0}} is a vector of zeros and a subset of p B {\displaystyle p_{B}} relevant parameters are equally responsible for a perfect fit of R 2 = 1 {\displaystyle R^{2}=1}, then this subset is activated at a λ {\displaystyle \lambda } value of 1 p {\displaystyle {\frac {1}{p}}}. The moment of activation of a relevant regressor then equals 1 p 1 p B p B 1 p B = 1 p {\displaystyle {\frac {1}{p}}{\frac {1}{\sqrt {p_{B}}}}p_{B}{\frac {1}{\sqrt {p_{B}}}}={\frac {1}{p}}}. In other words, the inclusion of irrelevant regressors delays the moment that relevant regressors are activated by this rescaled lasso. The adaptive lasso and the lasso are special cases of a '1ASTc' estimator. The latter only groups parameters together if the absolute correlation among regressors is larger than a user-specified value.