  With a focus on linear models with smooth functional covariates, we propose a
penalization framework (SACR) based on the nonzero centered ridge, where the
center of the penalty is optimally reweighted in a supervised way, starting
from the ordinary ridge solution as the initial centerfunction. In particular,
we introduce a convex formulation that jointly estimates the model's
coefficients and the weight function, with a roughness penalty on the
centerfunction and constraints on the weights in order to recover a possibly
smooth and/or sparse solution. This allows for a non-iterative and continuous
variable selection mechanism, as the weight function can either inflate or
deflate the initial center, in order to target the penalty towards a suitable
center, with the objective to reduce the unwanted shrinkage on the nonzero
coefficients, instead of uniformly shrinking the whole coefficient function. As
empirical evidence of the interpretability and predictive power of our method,
we provide a simulation study and two real world spectroscopy applications with
both classification and regression.
