用符号化非线性函数扩展生存分析模型,兼顾精度与可解释性。
Extending Cox Proportional Hazards Model with Symbolic Non-Linear Log-Risk Functions for Survival Analysis
- 基于KAN构建符号化非线性风险函数,替代传统线性组合。
- 在合成数据和多个公开基准上表现优于现有方法。
- 适合需要高可解释性的医疗生存分析场景。
Cox比例风险(CPH)模型广泛用于生存分析,通过多变量估计相对风险。传统CPH模型依赖协变量的线性组合作为对数风险函数,假设严格且限制性强,影响泛化能力。近年深度学习虽能实现非线性对数风险函数,但因端到端训练缺乏可解释性。柯尔莫哥洛夫-阿诺德网络(KAN)为构建完全透明、符号化的非线性对数风险函数提供了新可能。本文提出广义Cox比例风险(GCPH)模型,利用KAN实现从协变量到生存结果的符号化非线性映射。GCPH在保持传统CPH模型可解释性的同时,支持非线性对数风险估计。在合成数据及多个公共基准上的实验表明,GCPH在预测准确率上表现优异,且可解释性显著优于当前先进方法。
原文摘要 · Abstract (English)
The Cox proportional hazards (CPH) model has been widely applied in survival analysis to estimate relative risks across different subjects given multiple covariates. Traditional CPH models rely on a linear combination of covariates weighted with coefficients as the log-risk function, which imposes a strong and restrictive assumption, limiting generalization. Recent deep learning methods enable non-linear log-risk functions. However, they often lack interpretability due to the end-to-end training mechanisms. The implementation of Kolmogorov-Arnold Networks (KAN) offers new possibilities for extending the CPH model with fully transparent and symbolic non-linear log-risk functions. In this paper, we introduce Generalized Cox Proportional Hazards (GCPH) model, a novel method for survival analysis that leverages KAN to enable a non-linear mapping from covariates to survival outcomes in a fully symbolic manner. GCPH maintains the interpretability of traditional CPH models while allowing for the estimation of non-linear log-risk functions. Experiments conducted on both synthetic data and various public benchmarks demonstrate that GCPH achieves competitive performance in terms of prediction accuracy and exhibits superior interpretability compared to current state-of-the-art methods.
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