# Smoothly Adaptively Centered Ridge Estimator

arXiv: https://arxiv.org/abs/2011.00289 · HTML: https://mlsanity.com/paper/2011.00289/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2020.

## Built on by (most cited first, 2 of 2)

- [Nonconvex Penalized LAD Estimation in Partial Linear Models with DNNs: Asymptotic Analysis and Proximal Algorithms](https://mlsanity.com/paper/2511.21115/) (2025)
- [Sparse Bayesian Deep Functional Learning with Structured Region Selection](https://mlsanity.com/paper/2602.20651/) (2026)

## Abstract (arXiv)

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.