Pathological Regularization Regimes in Classification Tasks

TL;DR

This paper investigates the phenomenon of trend reversal in classification tasks caused by specific regularization parameters, providing algebraic conditions for ridge regression and insights for logistic regression to avoid such issues.

Contribution

It introduces the concept of pathological regularization regimes, offers algebraic criteria for ridge regression, and connects these findings to datasets with Simpson's paradox.

Findings

Identifies conditions for trend reversal in ridge regression

Provides practical tools to avoid pathological regimes

Links datasets with Simpson's paradox to regularization issues

Abstract

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.