A Ridge Too Far: Correcting Over-Shrinkage via Negative Regularization
arXiv stat.ML / 4/21/2026
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Key Points
- Conventional (positive) regularization is meant to reduce variance, but for small-data regression it can worsen underfitting when the useful predictive signal lies in weak directions of a restricted representation.
- The paper analyzes a “negative-capable” ridge regression family that allows a feasible negative regularization region while keeping the estimator well-posed.
- Within that negative region, negative regularization functions as controlled anti-shrinkage by increasing effective model complexity most strongly along weak eigen-directions.
- The authors formalize weak-spectrum underfitting, prove a sign-switch phenomenon under conservative baseline shrinkage, and propose a criterion-based method to automatically select regularization across the full negative-capable family.
- Experiments on synthetic and semi-synthetic data validate key theoretical claims, including feasibility of the negative region, spectral complexity growth, sign-switch behavior, and recovery of negative adjustments when appropriate.
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