# Pathological Regularization Regimes in Classification Tasks

arXiv: https://arxiv.org/abs/2406.14731 · HTML: https://mlsanity.com/paper/2406.14731/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 25 references that are in the map.
- First posted on arXiv 20 Jun 2024.

## Builds on (most cited first, 3 of 3)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [The Impact of Regularization on High-dimensional Logistic Regression](https://mlsanity.com/paper/1906.03761/) (2019)
- [Lecture notes on ridge regression](https://mlsanity.com/paper/1509.09169/) (2015)

## Abstract (arXiv)

In this paper we demonstrate the possibility of a trend reversal in binary classification tasks between the dataset and a classification score obtained from a trained model. This trend reversal occurs for certain choices of the regularization parameter for model training, namely, if the parameter is contained in what we call the pathological regularization regime. For ridge regression, we give necessary and sufficient algebraic conditions on the dataset for the existence of a pathological regularization regime. Moreover, our results provide a data science practitioner with a hands-on tool to avoid hyperparameter choices suffering from trend reversal. We furthermore present numerical results on pathological regularization regimes for logistic regression. Finally, we draw connections to datasets exhibiting Simpson's paradox, providing a natural source of pathological datasets.