In multiple regression problems when covariates can be naturally grouped, it is important to carry out feature selection at the group and within-group individual variable levels simultaneously. The existing methods, including the lasso and group lasso, are designed for either variable selection...

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual square and scaling the penalty in proportion to the estimated...