让逻辑回归更抗数据分布变化，速度提升408倍
Mixed-feature Logistic Regression Robust to Distribution Shifts
- 基于图结构设计新算法，可处理不同特征的分布偏移差异
- 相比现有方法，校准误差降低超四成，AUC提升近50%
- 适合需要稳定预测的高风险领域，如医疗与社会政策
逻辑回归因简洁可解释而广泛应用于社会科学与高风险场景，但这些领域常面临训练与部署时数据分布变化的问题。本文提出一种分布鲁棒逻辑回归模型，旨在应对从特定构造的Wasserstein模糊集生成的对抗性分布变化。与以往工作不同，本方法能捕捉特征间分布偏移概率差异，显著拓展适用范围。我们提出基于图的求解方法，可嵌入主流优化求解器。在多个公开数据集上的实验表明，该方法相较现有最优方案提速408倍；平均校准误差降低36.19%，最差情况下降41.70%；平均AUC提升18.02%，最差情况提升48.37%。
原文摘要 · Abstract (English)
Logistic regression models are widely used in the social and behavioral sciences and in high-stakes domains, due to their simplicity and interpretability properties. At the same time, such domains are permeated by distribution shifts, where the distribution generating the data changes between training and deployment. In this paper, we study a distributionally robust logistic regression problem that seeks the model that will perform best against adversarial realizations of the data distribution drawn from a suitably constructed Wasserstein ambiguity set. Our model and solution approach differ from prior work in that we can capture settings where the likelihood of distribution shifts can vary across features, significantly broadening the applicability of our model relative to the state-of-the-art. We propose a graph-based solution approach that can be integrated into off-the-shelf optimization solvers. We evaluate the performance of our model and algorithms on numerous publicly available datasets. Our solution achieves a 408x speed-up relative to the state-of-the-art. Additionally, compared to the state-of-the-art, our model reduces average calibration error by up to 36.19% and worst-case calibration error by up to 41.70%, while increasing the average area under the ROC curve (AUC) by up to 18.02% and worst-case AUC by up to 48.37%.
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