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arXiv · 2508.17412

A Ridge Too Far: Correcting Over-Shrinkage via Negative Regularization

Dongseok Kim·Gisung Oh
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Abstract

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.

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Dongseok Kim, Gisung Oh. 2025-08-24. A Ridge Too Far: Correcting Over-Shrinkage via Negative Regularization. https://arxiv.org/abs/2508.17412

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