用鲁棒优化提升生存分析模型的准确性和抗干扰能力
Distributionally Robust Learning in Survival Analysis
- 基于Wasserstein距离构建不确定集，改进Cox回归的鲁棒性
- 在真实数据和模拟实验中均优于传统方法，提升预测精度
- 适合医疗数据分析等对模型稳定性要求高的场景
我们提出一种将分布鲁棒学习（DRL）引入Cox回归的新方法，以增强生存预测的稳健性与准确性。通过采用基于Wasserstein距离的不确定性集构建DRL框架，开发出对底层数据分布假设不敏感、对模型误设和数据扰动更具韧性的一种变体Cox模型。利用Wasserstein对偶性，将原始的极小极大问题转化为可计算的正则化经验风险最小化问题，可通过指数锥规划求解。我们提供了所提DRL-Cox模型在有限样本下的理论保证。通过大量仿真及真实世界案例研究，验证了该模型在预测精度和鲁棒性方面均显著优于传统方法。
原文摘要 · Abstract (English)
We introduce an innovative approach that incorporates a Distributionally Robust Learning (DRL) approach into Cox regression to enhance the robustness and accuracy of survival predictions. By formulating a DRL framework with a Wasserstein distance-based ambiguity set, we develop a variant Cox model that is less sensitive to assumptions about the underlying data distribution and more resilient to model misspecification and data perturbations. By leveraging Wasserstein duality, we reformulate the original min-max DRL problem into a tractable regularized empirical risk minimization problem, which can be computed by exponential conic programming. We provide guarantees on the finite sample behavior of our DRL-Cox model. Moreover, through extensive simulations and real world case studies, we demonstrate that our regression model achieves superior performance in terms of prediction accuracy and robustness compared with traditional methods.
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