Smoothly Adaptively Centered Ridge Estimator
This work addresses the issue of improved coefficient estimation in functional data analysis for applications like spectroscopy, though it appears incremental as it builds upon existing ridge regression methods.
The authors tackled the problem of unwanted uniform shrinkage in linear models with functional covariates by proposing the Smoothly Adaptively Centered Ridge (SACR) estimator, which optimally reweights the penalty center to reduce shrinkage on nonzero coefficients, and demonstrated its interpretability and predictive power through simulations and real-world spectroscopy applications.
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.