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.

该研究论文通过展示训练模型获得的分类分数与数据集之间的趋势逆转的可能性，阐述了模型训练中正则化参数的选择对趋势逆转发生的影响，提供数据科学从业者避免遭受趋势逆转的超参数选择的实用工具，并通过逻辑回归在病态正则化区间上的数值结果，从路径性数据集的角度探讨了辛普森悖论的关联。