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Main Authors: Kim, Dongseok, Oh, Gisung
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2508.17412
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author Kim, Dongseok
Oh, Gisung
author_facet Kim, Dongseok
Oh, Gisung
contents Conventional regularization is designed to control variance, but in small-data regression it can also aggravate underfitting when predictive signal is concentrated in weak directions of a restricted representation. We study a negative-capable ridge family that permits a feasible negative region whenever the estimator remains well posed, and show that negative regularization acts there as controlled anti-shrinkage by increasing effective complexity most strongly along weak eigendirections. Building on this mechanism, we formalize weak-spectrum underfitting, derive a sign-switch result under conservative baseline shrinkage, and study criterion-based automatic selection over the full negative-capable family. Synthetic and semi-synthetic experiments support the theory by verifying feasibility, spectral complexity increase, sign-switch behavior, and effective recovery of negative adjustments in the predicted regimes.
format Preprint
id arxiv_https___arxiv_org_abs_2508_17412
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Ridge Too Far: Correcting Over-Shrinkage via Negative Regularization
Kim, Dongseok
Oh, Gisung
Machine Learning
Artificial Intelligence
Conventional regularization is designed to control variance, but in small-data regression it can also aggravate underfitting when predictive signal is concentrated in weak directions of a restricted representation. We study a negative-capable ridge family that permits a feasible negative region whenever the estimator remains well posed, and show that negative regularization acts there as controlled anti-shrinkage by increasing effective complexity most strongly along weak eigendirections. Building on this mechanism, we formalize weak-spectrum underfitting, derive a sign-switch result under conservative baseline shrinkage, and study criterion-based automatic selection over the full negative-capable family. Synthetic and semi-synthetic experiments support the theory by verifying feasibility, spectral complexity increase, sign-switch behavior, and effective recovery of negative adjustments in the predicted regimes.
title A Ridge Too Far: Correcting Over-Shrinkage via Negative Regularization
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2508.17412